Question

A number consists of two digits. The digit in the ten’s place exceeds the digit in the unit’s place by 4. The sum of the digits is \(\frac17\) of the number. The number is : 

(a) 27 

(b) 72 

(c) 48 

(d) 84

Answer 1

(d) Let the digit in the unit’s place = x 

Let the digit in the ten’s place = x + 4

∴ The number is 

10(x + 4) + x = 10x + 40 +x = 11x + 40

Sum of the digits = x + x + 4 = 2x + 4 

Given, 2x + 4 = \(\frac17\) (11x + 40)

⇒ 14x + 28 = 11x + 40 ⇒ 3x = 12 ⇒ x = 4

∴ The number is 11 × 4 + 40 = 44 + 40 = 84