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Important Questions Test: Ratio & Proportion- 3 - CAT MCQ


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14 Questions MCQ Test Quantitative Aptitude (Quant) - Important Questions Test: Ratio & Proportion- 3

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Important Questions Test: Ratio & Proportion- 3 - Question 1

Shalaj and Associates, a shoe-manufacturing company, has three machines producing shoes. If machine X produces l/4th as many as machine Y produces in the same time, and machine Y produces twice as many as machine Z produces in the same time, then during a fixed time, what fraction of the total number of shoes is produced by machine Z?

Detailed Solution for Important Questions Test: Ratio & Proportion- 3 - Question 1

► Assume that Y produces 4P units in unit time.
► Then X and Z produce P and 2P units in the same time.
► So, Total shoes produced = 7P, Fraction of the total number of shoes produced by machine Z = 2/7

Important Questions Test: Ratio & Proportion- 3 - Question 2

The inhabitants of Hawaii Island are taxed in a peculiar manner. They have to pay a fixed sum irrespective of their income strata. In addition to this they have to pay an amount which is proportional to the excess of their salary over Rs 50,000. Mr Kalyan pays a total tax of Rs 6,200 when his annual salary is Rs 60,000 and his wife Mrs. Kalyan pays a total tax of Rs 7,700 when her annual salary is Rs 75,000. What is the yearly salary of Mr Ajay who pays an annual tax of Rs 8,200?

Detailed Solution for Important Questions Test: Ratio & Proportion- 3 - Question 2

Tax = Fixed + Variable

► Since Mr Kalyan pays Rs 6200 and Mrs Kalyan pays Rs 7700, so it can be inferred that for Rs 10,000 (Difference between their salaries), one has to pay Rs 1500 as the variable tax.
► So, Fixed component of tax = Rs 5200. The point worth to be noted here is the fact that tax is to be paid over an above Rs 50,000.
► So, the variable tax percentage above Rs 50,000 = 10%. Now the answer can be calculated using options.

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Important Questions Test: Ratio & Proportion- 3 - Question 3

The speed of man while walking, running and driving are in the ratio of 1:3:9. If he travels equal distance while walking, running and driving, what is the ratio

Detailed Solution for Important Questions Test: Ratio & Proportion- 3 - Question 3

► Assume the distance = 9 units.
► So, the ratio of the time taken = 9:3:1
So, the answer = (9/1):(3/3):(1/9)
⇒ 81:9:1

Important Questions Test: Ratio & Proportion- 3 - Question 4

The time period of oscillation T for a pendulum is given

where l is the length of the pendulum and g is the acceleration due to gravity, ‘k’ is any const. If ‘k’ and ‘g’ remain unchanged under any condition, what should be the percentage change in l such that the time period T increases by 10%?

Detailed Solution for Important Questions Test: Ratio & Proportion- 3 - Question 4

T = 2π * (√l/g)

T increases by 10%, new time period 0.1T

(1T + 0.1T) = 2π * (√l/g)

1.1T = 2π * (√l/g)

i.e 21% increase in the length of the pendulum.

Important Questions Test: Ratio & Proportion- 3 - Question 5

Price of each article of type P, Q, and R is Rs. 300, Rs. 180 and Rs. 120 respectively. Suresh buys articles of each type in the ratio 3:2:3 in Rs. 6480. How many articles of type Q did he purchase?

Detailed Solution for Important Questions Test: Ratio & Proportion- 3 - Question 5

► Let the common factor be k.
► Hence, the number of articles of type P, Q and R will be 3k, 2k and 3k respectively
► Also, Unit price of article x Number of articles = Total amount for the articles
∴ 300 x 3k + 180 x 2k + 120 x 3k = 6480
⇒ k = 4
∴ Number of articles of Type Q = 2k = 8

Important Questions Test: Ratio & Proportion- 3 - Question 6

Read the passage below and solve the questions based on it.
In a class, every student plays exactly one of the following games—squash, table tennis, hockey, handball, cricket. Exactly 1/ 12th of the girls and 1/8th of the boys play- squash. 1/15th of the girls and 1/6th of the boys play hockey, 1/4th of the girls and 1/12th of the boys play handball. 1/5th of the girls and 3/8th of the boys plays table tennis and the remaining boys and girls play cricket. The total strength of the class is less than 120
Q. How many girls are there in the class?

Detailed Solution for Important Questions Test: Ratio & Proportion- 3 - Question 6

► Whatever is the total number of boys, it should be divisibie by 8, 6, 12 
► For total number of girls should be divisible by 12, 15 and 4, Now use options.

Important Questions Test: Ratio & Proportion- 3 - Question 7

Read the passage below and solve the questions based on it.
In a class, every student plays exactly one of the following games—squash, table tennis, hockey, handball, cricket. Exactly 1/ 12th of the girls and 1/8th of the boys play- squash. 1/15th of the girls and 1/6th of the boys play hockey, 1/4th of the girls and 1/12th of the boys play handball. 1/5th of the girls and 3/8th of the boys plays table tennis and the remaining boys and girls play cricket. The total strength of the class is less than 120
Q. Which of the following cannot be the ratio of boys and girls in the class?

Detailed Solution for Important Questions Test: Ratio & Proportion- 3 - Question 7

► Whatever is the total number of boys, it should be divisibie by 8, 6 and 12 
► For total number of girls should be divisible by 12, 15 and 4, Now use options.

Important Questions Test: Ratio & Proportion- 3 - Question 8

The expenses of a hostel are partly fixed and partly variable with the number of boarders. When there are 50 boarders the charge is Rs. 48 per head and when there are 30 boarders the charge is Rs. 60 per head. Find the charges when there are 120 boarders?

Detailed Solution for Important Questions Test: Ratio & Proportion- 3 - Question 8

Important Questions Test: Ratio & Proportion- 3 - Question 9

There are two drums, each containing a mixture of paints A and B. In drum 1, A and B are in the ratio 18 : 7. The mixtures from drums 1 and 2 are mixed in the ratio 3 : 4 and in this final mixture, A and B are in the ratio 13 : 7. In drum 2, then A and B were in the ratio

Detailed Solution for Important Questions Test: Ratio & Proportion- 3 - Question 9

It is given that in drum 1, A and B are in the ratio 18 : 7.

Let us assume that in drum 2, A and B are in the ratio x : 1.

It is given that drums 1 and 2 are mixed in the ratio 3 : 4 and in this final mixture, A and B are in the ratio 13 : 7.

By equating concentration of A

Therefore, we can say that in drum 2, A and B are in the ratio 239/161 : 1 or 239 : 161.

Important Questions Test: Ratio & Proportion- 3 - Question 10

The scores of Amal and Bimal in an examination are in the ratio 11 : 14. After an appeal, their scores increase by the same amount and their new scores are in the ratio 47 : 56. The ratio of Bimal’s new score to that of his original score is

Detailed Solution for Important Questions Test: Ratio & Proportion- 3 - Question 10

Let the score of Amal and Bimal be 11k and 14k
Let the scores be increased by x
So, after increment, Amal’s score =  11k + x and Bimal’s score = 14k + x
According to the question, 
On solving, we get x = 42/9 k
Ratio of Bimal’s new score to his original score

Hence, option A is the correct answer.

Important Questions Test: Ratio & Proportion- 3 - Question 11

Raju and Lalitha originally had marbles in the ratio 4:9. Then Lalitha gave some of her marbles to Raju. As a result, the ratio of the number of marbles with Raju to that with Lalitha became 5:6. What fraction of her original number of marbles was given by Lalitha to Raju?

Detailed Solution for Important Questions Test: Ratio & Proportion- 3 - Question 11

Let the number of marbles with Raju and Lalitha initially be 4x and 9x.
Let the number of marbles that Lalitha gave to Raju be a.

It has been given that (4x+a)/(9x-a) = 5/6
24x + 6a = 45x – 5a
11a = 21x
a/x = 21/11

Fraction of original marbles given to Raju by Lalitha = a/9x (Since Lalitha had 9x marbles initially).
a/9x = 21/99
= 7/33.

Therefore, option D is the right answer.

Important Questions Test: Ratio & Proportion- 3 - Question 12

Consider three mixtures - the first having water and liquid A in the ratio 1:2, the second having water and liquid B in the ratio 1:3, and the third having water and liquid C in the ratio 1:4. These three mixtures of A, B, and C, respectively, are further mixed in the proportion 4: 3: 2. Then the resulting mixture has

Detailed Solution for Important Questions Test: Ratio & Proportion- 3 - Question 12

The proportion of water in the first mixture is 1/3
The proportion of Liquid A in the first mixture is 2/3
The proportion of water in the second mixture is 1/4
The proportion of Liquid B in the second mixture is 3/4
The proportion of water in the third mixture is 1/5
The proportion of Liquid C in the third mixture is 4/5
As they are mixed in the ratio 4:3:2, the final amount of water is

The final amount of Liquid A in the mixture is 4 x 2/3 = 8/3
The final amount of Liquid B in the mixture is 3 x 3/4 = 9/4
The final amount of Liquid C in the mixture is 2 x 4/5 = 8/5
Hence, the ratio of Water : A : B : C in the final mixture is

From the given choices, only option C  is correct.

Important Questions Test: Ratio & Proportion- 3 - Question 13

If a, b, c are three positive integers such that a and b are in the ratio 3 : 4 while b and c are in the ratio 2:1, then which one of the following is a possible value of (a + b + c)?

Detailed Solution for Important Questions Test: Ratio & Proportion- 3 - Question 13

a : b = 3:4 and b : c = 2:1 => a:b:c = 3:4:2

=> a = 3x, b = 4x , c = 2x
=> a + b + c = 9x

=> a + b + c is a multiple of 9.
From the given options only, option C is a multiple of 9

Important Questions Test: Ratio & Proportion- 3 - Question 14

A stall sells popcorn and chips in packets of three sizes: large, super, and jumbo. The numbers of large, super, and jumbo packets in its stock are in the ratio 7 : 17 : 16 for popcorn and 6 : 15 : 14 for chips. If the total number of popcorn packets in its stock is the same as that of chips packets, then the numbers of jumbo popcorn packets and jumbo chips packets are in the ratio

Detailed Solution for Important Questions Test: Ratio & Proportion- 3 - Question 14

The ratio of L, S, J for popcorn = 7 : 17 : 16
Let them be 7x, 17x, and 16x
The ratio of L, S, J for chips = 6 : 15 : 14
Let them 6y, 15y and 14y
Given, 40x = 35y, x = 7y/8
Jumbo popcor = 16x = 16 * 7y/8 = 14y
Hence, the ratio of jumbo popcorn and jumbo chips = 1 : 1

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