If the nine - digit number 23541y49x is divisible by 72 then, (3x + 5y) : (5x + 3y) is equal to:
Show answer & explanation
Correct answer: A
Explanation
The correct answer is option 1 i.e. 7 : 9.
23541y49x is divisible by 72, 72 being the product of 8 and 9, which are two co-prime. So the number has to be divisible by both 8 and 9.
23541y49x is divisible by 8, if 49x is divisible by 8, which gives x = 6
The number becomes 23541y496, which will be divisible by 9 if the sum of the digits becomes divisible by 9
Now, (2 + 3 + 5 + 4 + 1 + y + 4 + 9 + 6) = 34 + y
⇒ y should be 2 so that the digit sum becomes (34 + 2 = 36) which is divisible by 9
For x = 6, y = 2
(3x + 5y) ∶ (5x + 3y)
⇒ (3 × 6 + 5 × 2) : (5 × 6 + 3 × 2)
⇒ (18 + 10) : (30 + 6)
⇒ 28 : 36 = 7 : 9