Chapter 7 - Ratio and Proportion (Including Properties and Uses) Exercise Ex. 7(C)

Question 1

If a : b = c : d, prove that:

(i) 5a + 7b : 5a - 7b = 5c + 7d : 5c - 7d.

(ii) (9a + 13b) (9c - 13d) = (9c + 13d) (9a - 13b).

(iii) xa + yb : xc + yd = b : d.

Solution 1

Question 2

If a : b = c : d, prove that:

(6a + 7b) (3c - 4d) = (6c + 7d) (3a - 4b).

Solution 2

Question 3

Given, , prove that:

Solution 3

Question 4

If ; then prove that:

x: y = u: v.

Solution 4

Question 5

If (7a + 8b) (7c - 8d) = (7a - 8b) (7c + 8d), prove that a: b = c: d.

Solution 5

Given, 

Applying componendo and dividendo,

Hence, a: b = c: d.

Question 6

(i) If x = , find the value of:

.

(ii) If a = , find the value of:

Solution 6

(i) x = 

(ii) 

Question 7

If (a + b + c + d) (a - b - c + d) = (a + b - c - d) (a - b + c - d), prove that a: b = c: d.

Solution 7

Question 8

If , show that 2ad = 3bc.

Solution 8

Question 9

If ; prove that: .

Solution 9

Given, 

Question 10

If a, b and c are in continued proportion, prove that:

Solution 10

Given, a, b and c are in continued proportion.

Question 11

Using properties of proportion, solve for x:

Solution 11

Question 12

If , prove that: 3bx² - 2ax + 3b = 0.

Solution 12

Since, 

Applying componendo and dividendo, we get,

Squaring both sides,

Again applying componendo and dividendo,

3bx² + 3b = 2ax

3bx² - 2ax + 3b = 0.

Question 13

Solution 13

Question 14

If , express n in terms of x and m.

Solution 14

Applying componendo and dividendo,

Question 15

If , show that:

nx = my.

Solution 15

Applying componendo and dividendo,