Questions :
When a two-digit number is multiplied by the sum of its digits, the product is 424. When the number obtained by interchanging its digits is multiplied by the sum of the digits, the result is 280. The sum of the digits of the given number is:
Options :
- 6
- 7
- 8
- 9
correct answer : c)
Let the two-digit number be 10x + y.
(10x + y)(x + y) = 424 …(I)
Number got by reversing the digits = 10y + x
(10y + x)(x + y) = 280 …(II)
Adding (I) and (II):
(10x + y)(x + y) + (10y + x)(x + y) = 424 + 280
⇒ (x + y)(10x + y + 10y + x)
= (x + y)(11x + 11y) = 704
⇒ 11(x + y)² = 704
⇒ (x + y)² = 64
⇒ (x + y) = √64 = 8