CAT Previous Year Questions: Ratio & Proportion (June 17) - CAT MCQ

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% 

Let the number of coins collected by A and B in one week be 3x and 4x respectfully.
The total number of coins collected by A in 5 weeks = 15x
For 15x to be a multiple of 7, x has to be a multiple of 7.
The total number of coins collected by B in 3 weeks = 12x
For 12x to be a multiple of 24, x has to be a multiple of 2.
Therefore, x has to be a multiple of 7 × 2 = 14
The minimum value that x can take is 14.
So, the minimum coins collected by A in one week = 3x = 3 × 14 = 42.

The ratio of the number of persons standing ahead of Pinky to the number of persons standing behind her in the queue is 3 : 5.

Let’s assume that there are 3x number of people ahead of Pinky, then the number of people behind her will be 5x.

The total number of people in the queue is 8x + 1.

Since the total number of people in the queue is less than 300.

8x + 1 < 300

x ≤ 37

To find the maximum number of people ahead of Pinky, we take the maximum possible value of x, which is 37.

Therefore, the maximum number of people ahead of Pinky is 3 * 37 = 111

The ratio of the number of males to females is 5 : 4
The ratio of the number of literate males to literate females is 2 : 3.
The ratio of the number of illiterate males to illiterate females is 4 : 3.
Let,
The number of males to females is 5x, 4x
The number of literate males to literate females is 2y, 3y.
The number of illiterate males to illiterate females is 4z, 3z.

We know that the ratio of the number of males to females is 5 : 4

4(2y + 4z) = 5(3y + 3z)
8y + 16z = 15y + 15z
z = 7y

3600 males in the village are literate.
2y = 3600
y = 1800
Total number of females = 24y = 24(1800) = 43,200

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.

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%