Question

A natural number P is multiplied by 11 and 33 is added to it. This sum is divided
by 9 and the remainder is zero. Select the smallest value of P that satisfies given
conditions.
put the
PX11+33​

Answer 1

Given info : A natural number P is multiplied by 11 and 33 is added to it. This sum is divided

by 9 and the remainder is zero.

To find : find the smallest value of P that satisfies given conditions.

solution : a/c to question,

number = P × 11 + 33 = 11P + 33 , this number is divided by 9 and the remainder is zero.

it means (11P + 33) is divisible by 9.

and we know, any number is divisible by 9 only when sum of all digits of the number is divisible by 9.

so, (1 + 1 + P + 3 + 3) = 8 + P is divisible by 9.

if P = 1 ⇒ 8 + 1 = 9 it is divisible by 9.

so the smallest value of P is 1 that satisfies the given conditions.