Hello CAT aspirants! As the CAT exam approaches, it’s the right time to focus on shortcuts and quick methods to tackle the Quantitative Aptitude section. You already know that out of 22 questions in CAT QA, around 8–10 questions come from arithmetic. That’s why learning effective arithmetic shortcuts is crucial to boost your speed and accuracy. In this article, you’ll learn how one simple formula can help you solve 5 different types of arithmetic questions, making your preparation smarter and more efficient for CAT 2025.

This Story also Contains

Importance of Arithmetic in CAT
The Magic Formula 1: Percentage Change
The Magic Formula 2: Weighted Average
Why These Shortcuts Work
Previous Years Questions
Best resources & practice material for CAT Number System
CAT 2025 Preparation Resources by Careers360

CAT 2025 Arithmetic Shortcuts: 1 Formula to Solve 5 Types of Questions

CAT Arithmetic Shortcuts 2025

Importance of Arithmetic in CAT

As discussed above arithmetic has a significant topicwise weightage in CAT Quantitative Aptitude section. It makes almost 40% – 45% of the total questions asked in CAT QA. You need to focus on each topic of arithmetic to ace this section.

To know the syllabus of QA section CAT, click on: Quantitative aptitude syllabus for CAT – 2025.

Important arithmetic topics for CAT

As arithmetic is very important to ace the QA section of CAT, we should know which topic we need to focus more on. Therefore, we should know the important topics and their weightage in recent years.

Important arithmetic topics for CAT are

Percentage	Profit and Loss	Simple interest and Compound interest
Average	Ratio and Proportion	Mixture and Alligation
Time, Speed, and Distance	Time and Work

For complete syllabus of CAT, visit CAT syllabus 2025.

Have a look at the number of questions asked in CAT from arithmetic during last 5 years.

S. No.	Year	Slot	Percentage and its application	Average, Ratio, and Mixture	TSD	Time and Work	Total
1	2020	1	3	3	4		11
2	2020	2	3	2	4	1	10
3	2020	3	3	3	3	1	10
4	2021	1	3	3	1	3	10
5	2021	2	4	2	1	2	9
6	2021	3	3	3	1	3	10
7	2022	1	4	2	1	2	9
8	2022	2	2	5	1	1	9
9	2022	3	1	4	3	2	10
10	2023	1	3	2	3	1	9
11	2023	2	3	4	1	1	9
12	2023	3	3	2	1	2	8
13	2024	1	3	3	1	1	8
14	2024	2	4	2	1	1	8
15	2024	3	4	3	1	1	9

The Magic Formula 1: Percentage Change

CAT arithmetic shortcuts are important to increase accuracy and save time. Here, we will discuss 1 formula to solve 5 CAT question types with short approach.

The formula:

$Final Value = Base or Initial Value \times (1 \pm \frac{Percentage Change}{100})$

Other form of this formula:

$Percentage Change = \frac{Final Value - Initial Value}{Initial Value} \times 100 %$

Applications of the Formula in 5 CAT question types

We are going to discuss application of percentage change formula in 5 different types of questions.

Type 1: To find the Percentage Increase or Decrease

This formula is used

To determine the percentage increase or decrease in population of a town
To solve the questions of depreciation or appreciation
To determine the percentage while comparing two values
To solve expenditure-based questions

Example:

A number is increased by 20% then by what percent it should be decreased to get the original value again?

Solution:

A number is increased by 20%: New Value = Initial Value × (1 + $\frac{20}{100}$ ) = Initial Value × 1.2

Required Percentage change: $Percentage Change = \frac{Change}{Base} \times 100 %$

= $\frac{Initial Value × 1.2 - Initial Value}{Initial Value × 1.2} \times 100 %$

= $\frac{0.2}{1.2} \times 100 %$

= $16.66 %$

Type 2: Application in Profit and Loss

This formula is used

To determine the selling price (Final Value) if Cost Price (Initial Value) and Profit or Loss percentage (Percentage Change) is given.
To determine the Profit or Loss percentage (Percentage Change) if selling price (Final Value) and Cost Price (Initial Value) is given.

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Example:

A shopkeeper buys an article at ₹1000 and gains 20%. Find Selling Price.

Solution:

Selling Price = 1000 × (1 + 0.2) = ₹1200

Similarly, if he makes a 20% loss:

Then Selling Price = 1000 × 0.8 = ₹800

3. Application in Simple Interest (SI)

Simple interest is equivalent to percentage change of the principal over time.

Example: Principal = ₹2000, Rate = 10%, Time = 3 years. Calculate amount after 3 years.

Solution:

To determine the Amount after 3 years, take percentage change = 10 × 3 = 30%

Now apply the percentage change formula;

Amount $= 2000 \times (1 + \frac{30}{100})$ = ₹2600

4. Application in Compound Interest (CI)

Repeated percentage change year after year gives the amount if interest is compounded annually.

Example:

Principal = ₹2000, Rate = 10% per annum compounded annually, Time = 3 years. Calculate the amount after 3 years.

Solution:

Amount after three years = $2000 \times (1 + \frac{10}{100}) \times (1 + \frac{10}{100}) \times (1 + \frac{10}{100})$ = ₹2662

Compound interest = ₹ (2662 – 2000) = ₹ 662

Tip → You can think of compound interest as successive percentage changes.

5. Application in Successive Percentage Change

Questions bases two or more consecutive changes (increase/decrease) can also be solved with the same principle.

Shortcut:

$Final Value = Initial Value(Base) \times (1 \pm \frac{a}{100}) \times (1 \pm \frac{b}{100})$

Example:

Price of an article increases by 20% and then decreases by 10%. Find net percentage change in the price of the article.

Solution:

Take Base Value or initial value = 100

$Final Value = 100 \times (1 + \frac{20}{100}) \times (1 - \frac{10}{100})$
$\Rightarrow Final Value = 100 \times 1.2 \times 0.9$
$\Rightarrow Final Value = 108$

Net effect = 8% increase.

The Magic Formula 2: Weighted Average

CAT arithmetic shortcuts are important to increase accuracy and save time. Here, we will discuss 1 formula to solve 5 CAT question types with short approach where average needs to be calculated.

The formula:

$Weighted average = \frac{Sum of Products of weights with average value}{Sum of Weights}$

Applications of the Formula in 5 CAT question types

We are going to discuss the application of weighted average in 5 different types of questions.

Type 1: To find the average value when two or more ingredients at different price are mixed in a given ratio

This formula is used

To determine the ratio of mixing two or more ingredients
To determine the average price when two or more quantities are added in a ratio
In milk and water problems

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Example:

If two varieties of wheats costing ₹40 and ₹60 are mixed in a ratio of 3 : 4 respectively, find the average price of wheat.

Solution:

Using the formula:

$Weighted average = \frac{Sum of Products of weights with average value}{Sum of Weights}$

$Required average price = \frac{40 \times 3 + 60 \times 4}{3 + 4} = 51.42$

Type 2: Application in Time, Speed, and Distance

This formula is used

To determine the average speed in TSD questions asked in CAT when different distances are covered at different speeds.

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Example:

Amit covers 80 km at 40 km/h and 120 km at 80 km/h. find his average speed for the journey.

Solution:

Time taken to cover 80 km at 40 km/h = 2 hrs

Time taken to cover 120 km at 80 km/h = 1.5 hrs

Using the formula:

$Weighted average = \frac{Sum of Products of weights with average value}{Sum of Weights}$

Weighted average formula is reduced to average ie. Average speed = $\frac{Total Distance}{Total time}$

$Average speed = \frac{80 + 120}{2 + 1.5} = 57.14$

Trick: If two equal distances are covered at different speeds, the average speed is the weighted harmonic mean.

Average speed = $\frac{Twice of product of speeds}{Sum of speeds}$

3. Application in Time and Work

When two or more workers having different efficiencies work together, their combined work rate is a weighted average of their individual rates.

Example: A can complete a job in 10 days, B in 20 days. In how many days they will finish the work together?

Solution:

To determine the 1-day work of A and B together, take weighted average

1 day work = $\frac{10 + 20}{10 \times 20} = \frac{3}{20}$

So, time taken = $\frac{20}{3}$ days

4. Application in Marks and Averages

The concept of weighted average is used when adding or removing, a student’s marks differ from average. Also, this concept is used to quick calculation of weighted average.

Example:

The average marks of 10 students is 40. A new student with 51 marks joins. Find the new average.

Solution:

Using the concept of weighted average, Ne average = $\frac{10 \times 40 + 51}{11} = \frac{451}{11} = 41$

5. Application in Profit & Loss

When two or more items purchased at same rate and sold at different profit/loss percentages, the net effect can be quickly found with the help of this formula.

Shortcut:

$Final Profit or loss percentage = \frac{Sum of all profit and loss percentages}{Number of items}$ , Here loss percentage is taken a s negative

Example:

A trader makes a profit of 25% on one item and loss of 15% on another, both of equal cost price. Find the overall profit or loss percentages.

Solution:

Using the above formula

$Final Profit percent = \frac{25 - 15}{2} = 5 %$

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Why These Shortcuts Work

These arithmetic shortcuts for CAT are necessary to ace Arithmetic section of CAT. If we look at the topics like Profit and loss, mixtures, SI and CI, all are looked different but in reality they can be reduced to a similar logic.

As we have seen, Profit and loss, SI and CI are extension of percentages. Mixtures is an extension of average. Time and Work is extension of average and ratio.

Percentage formula unifies all the topics like profit and loss, SI and CI. Average unifies all the five topics discussed above.

Key Advantages

It reduces time
No need to learn specific formulas for different concepts
It reduces confusion
It increases accuracy

Previous Years Questions

Q 1) During the first year, the population of the town increased by 12%. The next year, due to some contagious disease, it decreased by 8%. At the end of the second year, the population was 64,400. Find the population of the town at the beginning of the first year.

1) 50,000

2) 54,750

3) 62,500

4) 50,500

Solution:

Let the initial population be $x$ .

Then, according to the question,

The population increased by $12 %$

meaning the current population is $112 %$

of $x$ . Again the population decreased

meaning it is now $92 %$ of $112 %$ of $x$ .

So, $92 %$ of $112 %$ of $x = 64400$

$\Rightarrow 0.92 \times 1.12 x = 64400$

$\Rightarrow x = \frac{64400}{(0.92 \times 1.12)}$

$\Rightarrow x = \frac{64400}{1.0304}$

$\Rightarrow x = 62500$

Hence, the correct answer is 62,500.

Q 2) A notebook was sold for Rs. 28, at a profit of 12%. If it had been sold for Rs. 26.25, what would have been the profit percentage?

1) 5%

2) 7%

3) 4%

4) 6%

Solution:

Given: A notebook was sold for Rs. 28, at a profit of $12 %$ .

The selling price (SP) is Rs. 28 and the profit is $12 %$ .

Then, cost price (CP) is $\frac{S P \times 100}{100 + Profit %}$ .

So, $CP = \frac{28 \times 100}{100 + 12} = \frac{2800}{112} = 25$

If SP is Rs. 26.25, the profit

percentage will be $\frac{S P - C P}{C P} \times 100$

$= \frac{26.25 - 25}{25} \times 100 = 5 %$

Hence, the correct answer is $5 %$ .

Q 3) The interest on a certain deposit at $4.5 %$ p.a. is INR 135 in one year. How much will the additional interest in one year be on the same deposit at 5\% p.a.?

1) INR 16

2) INR 15

3) INR 14

4) INR 18

Solution:

Given: The interest on a certain deposit at $4.5 %$ p.a. is INR 135 in one year.

Let the principle be $P$ .

$Simple interest = \frac{Principal \times Rate \times Time}{100}$

$\Rightarrow 135 = \frac{P \times 4.5 \times 1}{100}$

$\Rightarrow P = \frac{13500}{4.5} = 3000$

On the same principle at a $5 %$ rate in 1 year,

Simple interest $= \frac{3000 \times 5 \times 1}{100} = 150$

So, the additional interest is $150 - 135 =$ INR 15

Hence, the correct answer is INR 15.

Q 4) A is 50% more efficient than B. B finished the same work in 20 days. If A and B worked together, then how much time would they take to finish the same work?

1) 10 days

2) 7 days

3) 8 days

4) 9 days

Solution:

Let the efficiency of B be 100 .

So, the efficiency of $A = 100 + 50 = 150$

The efficiency ratio of A and $B = 150$ :

$100 = 3 : 2$

Total efficiency $= 3 + 2 = 5$ units

The time taken by B to finish the work is 20 days.

So, Total work $=$ Efficiency of $B \times$ Time taken by B

$\Rightarrow Total work = 2 \times 20 = 40 units$

Time taken by $(A + B)$ to complete the work

$= \frac{Total work}{Total efficiency}$

$= \frac{40}{5}$

$= 8 days$

A and B together will finish the work in 8 days.

Hence, the correct answer is 8 days.

Q 5) Prasad goes 96 kilometres on a bike at a speed of 16 km/hr, 124 kilometres at 31 km/hr in a car, and 105 kilometres at 7 km/hr in a horse cart. Find his average speed for the entire distance travelled.

1) 16 km/hr

2) 13 km/hr

3) 7 km/hr

4) 11 km/hr

Solution:

Total distance travelled = $96 + 124 + 105 = 325 km$

Total time taken = $\frac{96}{16} + \frac{124}{31} + \frac{105}{7} = 6 + 4 + 15 = 25$ hours

Average speed = $\frac{Total distance}{Total time taken} = \frac{325}{25} = 13 km / hr$

Hence, the correct answer is $13 km / hr$ .

Best resources & practice material for CAT Number System

1. Arun Sharma: A Quantitative Approach for CAT (7th Edition)
2. Quantitative Aptitude for CAT by Nishit K Sinha

CAT 2025 Preparation Resources by Careers360

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eBook Title	Download Links
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Frequently Asked Questions (FAQs)

Q: How can we calculate average speed if a person travels with two different speeds for equal time?

Average speed in this case is equal to sum of the speeds divided by 2.

Q: What is the difference between average and weighted average?

Simple average is calculated when quantities are equal. Weighted average is calculated when quantities are not equal.

Q: Do I need to practice each application separately?

Although, you can use the same formula but you need to practice each application separately so that you can get familiar with the question type.

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Questions related to CAT

On Question asked by student community

Have a question related to CAT ?

which colleges near Gujarat accept exams CAT XAT SNAP CMAT my percentile for cat are 70 . suggest me according to that situation.

With a 70 percent in CAT Examination, you can go for various B-Schools or private collages. The S. K. Patel Institute of Management in Gandhinagar is an option for those who score 70-80 percent in their CAT examination or The Gujarat Institute of Management (GIM) in Goa with a cutoff of 60-80 percentage. These are the collages you can look for in Gujarat or nearby.

Collage in other regions: BA Colleges Accepting 70-80 Percentile in CAT 2025

Thank You.

Read Complete Answer

Amisha Soni

6 Oct'25

The obc ncl certificate i uploaded in my cat application shows my gender wrongly(a mistake from the issued authorities), will my cat application get rejected with this mistake, if not, will i be still considered as obc,as all other details in certificate is correct otherthan than this mistake.

Hello dear candidate,

NO. your application for CAT will not rejected for wrong gender small mistake in the OBC NCL certificate. You will be considered as an OBC candidate.

you just need to get your OBC certificate corrected and need to inform the CAT helpdesk about this error.

Read Complete Answer

Amisha Soni

5 Oct'25

Top mba colleges under 2 lakh budget with exam like cat cmat whichever they are accepting with their cutoff

Hello,

Here are some top MBA colleges in India with fees under Rs. 2 lakh and their exam/cutoff details:

SIMSREE, Mumbai – Fee around Rs. 1.3–1.4 lakh for 2 years. Accepts CAT, CMAT, MAH-CET, MAT, ATMA. Cutoff is very high, usually 99+ percentile in CAT/CMAT.
PUMBA (Dept. of Management Sciences, Savitribai Phule Pune University) – Fee around Rs. 1.2–1.3 lakh. Accepts CAT, CMAT, MAH-CET, ATMA. Cutoff approx. 75+ percentile in CAT, 90–95+ percentile in CMAT, high scores in MAH-CET.
TISS, Mumbai (MA HRM & other management-related programmes) – Fee around Rs. 1.7–1.9 lakh. Accepts CAT for some courses. Qualifying cutoff is around 60–70 percentile, but final selection cutoffs are higher.

These are the main government institutes where the full MBA/PG programme fee is within Rs. 2 lakh. Cutoffs vary slightly each year and by category, but SIMSREE and PUMBA generally need high scores, while TISS has its own process along with CAT shortlisting.

Hope it helps !

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Prachi Kumari

4 Oct'25

can i get admission in any BDS govt college in delhi through aic with neet score 344 .(st cat.)

Hey! With a NEET score of 344 in the ST category, it is highly unlikely to get admission in any government BDS college in Delhi through the All India Quota. The cutoff for government BDS seats in Delhi usually falls around 400–450 for ST category, so your score is below that range.

You can consider private dental colleges, state quota seats in other states, or reattempt NEET next year to improve your chances.

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Ankur Mehta

29 Sep'25

can i get admission in any BDS college in jandk through jkbopee councling with neet score 344 .(stk cat.)

Hello dear candidate,

YES, with NEET score 344in the ST category you have high chances of getting admission in a BDS College in J&K through JKBOPEE counselling.

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Thank you.

Popular CAT Questions

Directions for question :

M/s Deloitte Touche Tohmatsu Limited, one of the top four audit and accounting firms in the world with headquarters at London, UK, and with an operational presence in 153 countries, hires Management Trainees (MT) from all the premier management institutes of India thrice every year, in the months of January, May and September.

Each new group of Management Trainees (MT) have to go through a four month rigorous training schedule, after which they have to pass through a test consisting of a written assessment and a case-analysis. The top hundred ranked Management Trainees (MT) based on the performance in the test are confirmed as Management Executives (ME). The rest are given the opportunity of undergoing the training for four months one more time along with the next batch of Management Trainees (MT) and then passing through the subsequent test consisting of the written assessment and case-analysis. The Management Trainee (MT) who fails to get confirmed as a Management Executive (ME) the second time is fired.

The scatter-graph below depicts the number of Management Trainees (MT) at Deloitte taking the tests from January 2020 till May 2022, and the vis-à-vis hired Management Trainees (MT) at Deloitte who were fired :

It is also known that for the month of September 2019 at Deloitte, 96 hired Management Trainees (MT) failed to be confirmed as a Management Executive (ME) the first time, and that 36 hired Management Trainees (MT) were fired.

Question :

In which test did the minimum number of Management Trainees (MT) get confirmed as a Management Executive (ME) in the second attempt ?

Option: 1

September 2020

Option: 2

May 2021

Option: 3

January 2021

Option: 4

January 2022

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Directions for question:

Two friends Moloy and Niloy passed out from the Purulia Institute of Science and Technology with B.Tech degrees in Mechanical Engineering, but even after a year placement was hard to find. So they decided to take the challenge head-on, came down to Kolkata, rented a garage space on Park Street, and having an affinity towards making people enjoy good food, started their firm named 'B.Tech Bread-Omlette Wala'.

They started with three items on the menu. One was the French Toast which could be prepared in 3 minutes. The second was the Egg Tortillas which took 15 minutes to prepare. Any one of Moloy and Niloy could prepare any one of them at a time. The third was the Egg Bhurji with French Fries. This however was prepared on an automated fryer which could prepare 3 servings at a time and took 5 minutes irrespective of the number of servings equal to or below 3. The fryer did not need anyone to attend to it, and the time to put in the raw ingredients could be neglected. So one could tend to the preparation of other items while the Egg Bhurji with French Fries were being prepared.

They wanted to serve the orders as early as possible after the order was given. The individual items in any order were served as and when all the items were ready, and the order was then considered closed. None of the items on the menu were prepared in advance in anticipation of future orders.

On the first day, 3 groups of customers came in and ordered at 6.00 pm, 6.10 pm, and 6.13 pm. The first order was for a plate of Egg Tortillas, two plates of French Toast, and three plates of Egg Bhurji with French Fries. The second order was for a plate of French Toast and two plates of Egg Bhurji with French Fries. The third order was for a plate of Egg Tortilla and a plate of Egg Bhurji with French Fries.

On the backdrop of the above information answer the questions given :

Question:

Assuming that the next customer's order could only be attended to when the previous customer's order was closed, at what time would the first customer's order be considered closed ?

Option: 1

6.15 pm

Option: 2

6.17 pm

Option: 3

6.18 pm

Option: 4

6.20 pm

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Directions for question :

Six sticks of equal lengths were kept in the vertical position in an empty flower-vase, to be arranged at the six corners of a regular hexagon. The two ends of each of the sticks were of different colours.

The top ends of the sticks were one of each of the following colours – Red, Cyan, Pink, Brown, Black and Green. The bottom ends were one of each of the following colours – Blue, Yellow, White, Orange, Purple and Grey. Both the sets of colours mentioned were in no particular order.

It was also known that :

a) The stick with the red colour was opposite to the stick with the blue colour

b) There were exactly two sticks whose both ends had colours whose names started with the same letter

c) The stick with the grey colour was adjacent to the stick with the white colour

d) The stick with the cyan colour was adjacent to both the sticks with the brown colour and the one with the blue colour

e) The stick with the purple colour was adjacent to both the sticks with the grey colour and the one with the green colour

f) The stick with the white colour was opposite to the stick with the green colour

Question :

What was the colour of the bottom end of the stick having brown colour at the top end ?

Option: 1

White

Option: 2

Yellow

Option: 3

Black

Option: 4

Grey

Read Complete Answer

Directions for question:

On the backdrop of the above information answer the questions given :

Question:

Assuming that the next customer's order could only be attended to when the previous customer's order was closed, at what time would the third customer's order be considered closed ?

Option: 1

6.28 pm

Option: 2

6.35 pm

Option: 3

6.38 pm

Option: 4

6.45 pm

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Directions for question:

On the backdrop of the above information answer the questions given :

Question:

Suppose Moloy and Niloy had decided to process multiple orders at the same time, however strictly prioritising a first come first serve basis, when would the second customer's order be considered closed ?

Option: 1

6.20 pm

Option: 2

6.18 pm

Option: 3

6.15 pm

Option: 4

6.12 pm

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Directions for question:

On the backdrop of the above information answer the questions given :

Question:

Suppose Moloy and Niloy had decided to process multiple orders at the same time, however strictly prioritising a first come first serve basis, when would the third customer's order be considered closed ?

Option: 1

6.22 pm

Option: 2

6.25 pm

Option: 3

6.28 pm

Option: 4

6.30 pm

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Directions for question:

On the backdrop of the above information answer the questions given :

Question:

A fourth customer comes in and orders two plates of French Toast at 6.24 pm. Suppose Moloy and Niloy had decided to process multiple orders at the same time, however strictly prioritising a first come first serve basis. For exactly how many minutes would one of the friends be idle from 6.00 pm till serving the last customer, assuming that the four customers were the only ones to have come in within the period being discussed ?

Option: 1

Option: 2

Option: 3

Option: 4

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Directions for question:

On the backdrop of the above information answer the questions given :

Question:

Had Niloy been absent on that day, and assuming that the next customer's order could only be attended to when the previous customer's order was closed, at what time would the fourth customer's order (refer to the previous question) be considered closed ?

Option: 1

6:38 pm

Option: 2

6:42 pm

Option: 3

6:47 pm

Option: 4

6:49 pm

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Directions for question:

The bar-graph given below shows the foreign exchange reserves of Nepal (in million Rupees) from 2014 to 2021. Answer the following questions based on the graph :

Question:

What was the percentage increase (rounded to the nearest integer, if deemed necessary) in the foreign exchange reserves in 2020 over 2016 ?

Option: 1 None

Option: 2 None

Option: 3 None

Option: 4 None

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Directions for question:

The Jadavpur University’s Prince Anwar Shah Road hostel consists of two large separate buildings, one for the ladies and the other for the gents, while having a common kitchen and dining hall. It is the hostel of the CS and the EEC department of engineering students of the university.

In recognition of the growing dissatisfaction and hence complaints among the inmates of the hostel regarding the menu served for dinner, the Dean of the engineering department, Dr Aparesh Sanyal, personally decided to investigate the matter. He set about collecting information about the preference of dinner among the inmates, separately from the gents and the ladies wing of the hostel.

Dr Sanyal was able to gather the following partial information :

Hostel inmates	Menu preference for dinner			Total
Hostel inmates	Egg Meal	Fish Meal	Chicken Meal	Total
Gents			20
Ladies				64
Total		60

The Warden of the hostel was consulted, who after investigation declared that the following facts were clear :

1. Forty percent of the hostel inmates were ladies

2. One-third of the gentlemen inmates preferred an egg meal for dinner

3. Half the hostel inmates preferred either fish meal or chicken meal

Question:

What proportion of the lady hostel inmates preferred a fish meal for dinner ?

Option: 1

0.25

Option: 2

0.50

Option: 3

0.75

Option: 4

1.00

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