If P : Q = 1 2 : 1 3 and Q : R = 1 1 2 : 1 1 3 , find P : R .

Given, P : Q = 1 2 : 1 3 and Q : R = 1 1 2 : 1 1 3 , We are given to find P : R . We have, P : Q = 1 2 : 1 3 ⇒ P Q = 1 2 1 3 ⇒ P Q = 1 2 × 3 1 ⇒ P Q = 3 2 -----(i) Also, Q : R = 1 1 2 : 1 1 3 ⇒ Q : R = 3 2 : 4 3 ⇒ Q R = 3 2 4 3 ⇒ Q R = 3 2 × 3 4 ⇒ Q R = 9 8 -----(ii) Multiplying (i) by (ii), we obtain, P Q × Q R = 3 2 × 9 8 ⇒ P R = 27 16 ⇒ P : R = 27 : 16 Therefore, the required ratio P : R is 27 : 16 .

If 1 1 4 : 2 1 3 = p : q and q : r = 4 1 2 : 5 1 4 , find p : r .

Given, 1 1 4 : 2 1 3 = p : q and q : r = 4 1 2 : 5 1 4 . We have to find p : r . We have, 1 1 4 : 2 1 3 = p : q ⇒ p : q = 5 4 : 7 3 ⇒ p q = 5 4 7 3 ⇒ p q = 5 4 × 3 7 ⇒ p q = 15 28 -----(i) And, q : r = 4 1 2 : 5 1 4 ⇒ q : r = 9 2 : 21 4 ⇒ q r = 9 2 21 4 ⇒ q r = 9 2 × 4 21 ⇒ q r = 6 7 -----(ii) Multiplying (i) by (ii), we obtain, p q × q r = 15 28 × 6 7 ⇒ p r = 45 98 ⇒ p : r = 45 : 98 . Therefore, the required ratio p : r is 45 : 98 .

E M B I B E

Concise Mathematics Middle School Class 7>Chapter 6 - Ratio and Proportion>EXERCISE 6(B)

R K Bansal Solutions for Chapter: Ratio and Proportion, Exercise 2: EXERCISE 6(B)

Author:R K Bansal

R K Bansal Mathematics Solutions for Exercise - R K Bansal Solutions for Chapter: Ratio and Proportion, Exercise 2: EXERCISE 6(B)

Attempt the free practice questions on Chapter 6: Ratio and Proportion, Exercise 2: EXERCISE 6(B) with hints and solutions to strengthen your understanding. Concise Mathematics Middle School Class 7 solutions are prepared by Experienced Embibe Experts.