Ratio & Proportion CAT Previous Year Questions with Answer PDF

Let the number of total employees in the company be 100x, and the total salary of all the employees be 100y.

It is given that 20% of the employees work in the manufacturing department, and the total salary obtained by all the manufacturing employees is one-sixth of the total salary obtained by all the employees in the company.

Hence, the total number of employees in the manufacturing department is 20x, and the total salary received by them is (100y/6)

Average salary in the manufacturing department = (100y/6*20x) = 5y/6x

Similarly, the total number of employees in the nonmanufacturing department is 80x, and the total salary received by them is (500y/6)

Hence, the average salary in the nonmanufacturing department = (500y/6*80x) = 25y/24x

Hence, the ratio is:- (5y/6x): (25y/24x) 

⇒ 120: 150 = 4:5

Let the volume of mixture A be 200 ml, which implies the quantity of cocoa in the mixture is 120 ml, and the quantity of sugar In the mixture 80 ml.

Similarly, let the volume of the mixture be 300 ml, which implies the quantity of coffee, and sugar in the mixture is 210, and 90 ml, respectively.

Now we combine mixture A, and B in the ratio of 2:3 (if 200 ml mixture A, then 300 ml of mixture B).

Hence, the volume of the mixture C is (200+300) = 500 ml, and the quantity of the sugar is (90+80) = 170 ml. 

Now he mixes C with an equal amount of milk to make a drink, which implies the quantity of the final mixture is (500+500) = 1000 ml.

The quantity of sugar in the final mixture is 170 ml.

Hence, the percentage is 17% 

One candidate got 30% of the polled votes, the remaining three got in the ratio of 1 : 2 : 3
The polled votes were split in 3 : 7 ratio.
The 70% of them were again split in the ratio 1 : 2 : 3
The votes were polled in the ratio of 6(3) : 7(1 : 2 : 3)
18 : 7 : 14 : 21
Let’s assume that the actual polled votes are 18x, 7x, 14x, 21x
The winner of the election received 2512 votes more than the candidate with the second highest votes.
21x - 18x = 2512
3x = 2512
Total polled votes = 18x + 7x + 14x + 21x = 60x = 20(3x) = 20(2512) = 50,240
The polled votes represent 80% of the total registered votes.
Total registered votes = 50,240 + 12,560 = 62,800.

Given,

Let the speed of train 1 from A to B be s.
Then the speed of train 2 from A to B is 2s.
Time taken by train 1 to cover A to C = 
And, time taken by train 2 to cover A to C
= 
Required ratio = 

In 2010, Let the salary of Ramesh, Ganesh and Rajesh be 6x, 5x and 7x

Ramesh's salary increased by 25% during 2010 - 2015 = 6x × 125/100

⇒ 7.5x

But in 2015 the salaries ratio is 3 : 4 : 3 for Ramesh, Ganesh and Rajesh respectively

We can see in 2015, the salary of Ramesh and Rajesh is the same which is in the given ratio.

So, In 2015, the salary for Rajesh should also be 7.5x

Now percentage increase in the salary for Rajesh during 2010 - 2015 = [(7.5x - 7x)/7x] × 100

⇒ (0.5/7) × 100

⇒ 50/7

⇒ 7.14%

∴ The percentage increase in Rajesh’s salary during this period is closest to 7%.

Since scores of Anjali, Mohan and Rama after review were in the ratio of 11 : 10 : 3, therefore we can suppose scores of Anjali, Mohan and Rama after review be 11x, 10x and 3x respectively.

Therefore, their scores before review was (11x – 6), (10x – 6) and (3x – 6) respectively.

Since, Rama’s score was one-twelfth of the sum of the scores of Mohan and Anjali

⇒ 12 (3x – 6) = 21x – 12 ⇒ x = 4

Now, Anjali’s score – Rama’s score

= (11x – 6) – (3x – 6) = 8x = 8 × 4 = 32

Initial amount of salt in vessel A = 10 gms per 100 ml. solution. Therefore in 500 ml solution in vessel amount of salt = 50 gms

Similarly, initially in 500 ml solution in vessel B amount of salt = 110 gms

and initially in 500 ml solution in vessel C, amount of salt = 160 gms

When 100 ml is transferred from A to B, the amount of salt now in B = 10 + 110 = 120 gms in 600 ml.

The new concentration of salt in B = 120 / 600 x 100

= 20 gms per 100 ml.

Now, the amount of salt in A = 50 – 10 = 40 gms in 400 ml

Now, when 100 ml is transfered from B to C, the amount of salt now in C = 20 + 160 = 180 gms in 600 ml.

The new concentration of salt C = 180 / 600 x 100

= 30 gms per 100 ml

Finally, when 100 ml is transfered from C to A, the amount of salt now in A = 30 + 40 = 70 gms in 500 ml.

∴ Strength of salt in 70 / 500 x 100 = 14

Weight of liquid 1 per litre = 1000 gm

Weight of liquid 2 per litre = 800 gm

Weight of mixture per litre = 2 × 480 = 960 gm

By alligation rule,

Quantity of liquid 1 / Quantity of liquid 2 = = 4 / 1

Hence, the liquids are mixed in 4 : 1.

∴ Percentage of liquid 1 = (4 / 4 + 1) x 100 = 80%

Ratio of incomes of Amala, Bina and Gouri = 3 : 4 : 5

Ratio of interests of Amala, Bina and Gouri = 6 : 5 : 4

Therefore, the ratio of their interest income = (3 × 6) : (4 × 5) : (5 × 4) = 18 : 20 : 20

Let the interest incomes of Amala, Bina and Gouri be 18x, 20x and 20x respectively.

Since, Bina’s interest income exceeds Amala’s by Rs 250

Therefore, 20x – 18x = 250 ⇒ x = 125

Total interest incomes = 18x + 20x + 20x = 58x = 58 × 125 = 7250

Let the cost prices of A and B be Ca and Cb respectively.

Selling price of the mixture = 40 per kg.

The profit made is 10% if A and B are mixed in the ratio 3:2.

∴

⇒

The profit made is 5% if A and B are mixed in the ratio 2 : 3.

∴

⇒

Divide equation (i) by (ii), we get

⇒ 24Ca = 19Cb ⇒ Ca : Cb = 19 : 24

Let the numbers of marbles with Raju and Lalitha be 4x and 9x respectively.

Let Lalitha gave y marbles to Raju.

∴ ⇒  

Fraction of original marbles that Lalitha gave to Raju

= y / 9x = 7 / 33

Let the total no. of popcorn pockets in stock be T

Total no. of chips pockets in stock = T

Required ratio 

C₅ – C₁ = 19, the numbers above are the actual profits

∴ The total profit = 438 crore.