Question

18. The difference between two numbers is 23. Taking the larger number as x, find :
(1) the expression for smaller number.
(ii) the smaller number, if the sum of these two numbers is 91.​

Answer 1

Given

• The difference between two numbers is 23.

• The larger number is x.

(I) Hence, The smaller number would be x - 23 so that the difference between two numbers become 23.

(ii) If the sum of two numbers is 91, then

x + x - 23 = 91

=> 2x - 23 = 91

=> 2x = 91 + 23

=> 2x = 114

=> x = 57

Thus, the larger number = x = 57.

And the smaller number = x - 23 = 57 - 23 = 34.

Hence, the two number is 34 and 57 respectively.

Answer 2

Answer:

• Difference b/w two numbers = 23
• Larger number = x

(i) The expression for smaller number.

⇒ Difference b/w two numbers = 23

⇒ Larger number - Smaller number = 23

⇒ x - Smaller number = 23

⇒ x - 23 = Smaller number

⇒ Smaller number = x - 23

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(ii) The smaller number, if the sum of these two numbers is 91.

⇢ Sum of both numbers = 91

⇢ Larger number + Smaller number = 91

⇢ x + x - 23 = 91

⇢ 2x = 91 + 23

⇢ 2x = 114

• Dividing both by 2

⇢ x = 57

◗ Smaller number = x - 23 = (57 - 23) = 34