Correct Answer - Option 1 : 7 ∶ 9
Concept:
Divisibility by 9 = When the sum of the digits of a number is divisible by 9, the number is said to be divisible by 9.
Divisibility by 8 = When the last 3 digits of a number are divisible by 8, the number is said to be divisible by 8.
Given:
23541y49x is divisible by 72
Calculation:
23541y49x is divisible by 72, which is 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
∴ The required result = 7 : 9
