# Ratio & Proportion

29 April 2020

In Mathematics, concept of ratio and proportion plays a vital role. May it be calculation of Speed or calculation of  price (rupees/meter) of a material, the concept is required. Hence to solve various concepts, understanding the Ratio and proportion is important.

Ratio is the relative size of two quantities expressed as the quotient of one divided by the other; the ratio of a to b is written as a:b or a/b and Proportion is an equality between two ratios.

##### Practice Questions For Ratio & Proportion

Q1) Three beakers have capacity of 250ml, 650ml and 200ml. 682 ml of Juice is poured into them so that the same fraction of each is filled. The volume filled in the largest beaker will be:

A) 415 ml

B) 403 ml

C) 400 ml

D) 424 ml

Solution :

Q2) Two cogged wheels of which one has 32 cogs and other 54 cogs, work into each other. If the latter turns 80 times in three quarters of a minute, how often does the other turn in 8 seconds?

A) 48

B) 24

C) 38

D) None of these

Solution :

Q3) A and B together have Rs. 1210. If 4/15 of A's amount is equal to 2/5 of B's amount,  how much amount does B have?

A) Rs 460

B) Rs 484

C) Rs 550

D) Rs 550

Solution :

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Q4) A sum of money is to be distributed among A, B, C, D in the proportion of 5:2:4:3. If C gets Rs. 1000 more than D, what is B's share?

A) Rs. 500

B) Rs. 1500

C) Rs. 2000

D) None

Solution :

Q5) A got twice as many marks in English as in Science. His total marks in English, Science and Mathematics is 180. If the ratio of his marks in English and Mathematics is 2 : 3, what is his marks in Science?

A) 10

B) 20

C) 30

D) 40

Solution :

English : Mathematics = 2:3
English : Science = 2:1
English : Mathematics : Science = 2:3:1
English + Mathematics + Science = 180
Marks in Science = (1/6)*180 = 30

Q6) In a book store house, the ratio of English to hindi books is 7:2. If there are 1512 English books and due to increase in demand of English books, few English books are added by the shopkeeper and the said ratio become  15:4. The number of English books added is:

A) 432

B) 3024

C) 1620

D) 108

Solution :

---> The ratio of English books/Hindi books
---> 7 : 2 = 1512 : Hindi books
---> Hindi books = 432
---> Let x books are added:
---> 15 : 4 = (1512 + x) : 432
---> on solving we get x = 108

Q7) By mistake, instead of dividing Rs. 117 among A, B and C in the ratio 1/2,1/3,1/4 it was divided in the ratio of 2:3:4. Who gains the most and by how much?

A)  A, Rs. 28

B) B, Rs. 3

C) C, Rs. 20

D) C, Rs. 20

SOlution :

----> Original ratio of A, B, and C = 1/2 : 1/3 : 1/4 = 6: 4: 3
----> Share of A = 6/13 * 117 = Rs. 54
----> Share of B = 4/13 * 117 = Rs. 36
----> Share of C = 3/13 * 117 = Rs. 27
----> The ratio of A, B, and C by mistake = 2 : 3 : 4
----> Share of A = 2/9 *117 = Rs.26
----> Share of B = 3/9 *117 = Rs.39
----> Share of C = 13 * 4 = Rs.52
----> Therefore, it is clear from the above calculation that C gains maximum i.e.52 - 27 = Rs. 25

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Q8) Dhiraj have coins are in the ratio of Rs.1 coins, 50p coins and 25p coins can be expressed by three consecutive odd prime numbers that are in ascending order. The total value of coins in the bag is Rs 58. If the numbers of Rs.1, 50p, and 25p coins are reversed, find the new total value of coins in the bag of Dhiraj?

A) Rs.86

B) Rs. 83

C) Rs. 75

D) Rs. 82

Solution :

Since the ratio of the number of Rs. 1, 50p and 25p coins can be represented by 3 consecutive odd numbers that are prime in ascending order; the only possibility for the ratio is 3:5:7

---> Let the number of Rs.1, 50p and 25p coins be 3x, 5x and 7x respectively.

---> Hence, total value of coins in paise

---> = 100*3x+50*5x+25*7x = 725x

---> Given 725x = 5800
---> therefore x = 8

---> If the number of coins of Rs. 1,50p and 25p is reversed, the total value of coins in the Bag (in paise)

---> = 100*7x+50*5x+25*3x = 1025x

---> Substitute x = 8

---> New total = RS. 82

Q9) Karan, Hari and Kowshik play cricket. The runs got by Karan to Hari and Hari to Kowshik are in the ratio of 5:3. They get altogether 588 runs. How many runs did Karan get?

A) 150 runs

B) 300 runs

C) 250 runs

D) 200 runs

Solution :

Karan, Hari and Kowshik play cricket. The runs got by Karan to Hari and Hari to Kowshik are in the ratio of 5:3. They get altogether 588 runs. How many runs did Karan get:

Reference :

---> Karan : Hari = (5:3)

---> Hari : Kowshik = (5:3)

---> Karan : Hari : Kowshik = (25:15:9)

---> Therefore, the runs made by Karan,

---> = (25/49) * 588

---> = 25 * 12 = 300 runs

Q10) An outgoing batch of students wants to gift books worth Rs 4,200 to their teachers. If the boys, offer to pay 50% more than the girls and an external sponsors gives three times the boy’s contribution, then how much should the boys donate?

A) Rs 600

B) Rs 840

C) Rs 900

D) Rs 1,200

Solution :

----> The ratio of the share girls: boys: sponsors = (1:1.5:4.5)

----> So the proportion to boy’s share = (1.5/7)

----> Hence, the boys would donate = (1.5/7) * 4200 = Rs 900

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