Question
A student calculates the average of five two-digit numbers.
If one of them is reversed and the new average increases by 9, and all the numbers are consecutive multiples of 12, then what is the reversed number?Solution
ATQ,
Let the number which is reversed be (10a + b)
Then reversed = (10b + a)
As per question:
10b + a – 10a – b = 9 × 5
⇒ 9(b – a) = 45
⇒ b – a = 5
Now checking five consecutive multiples of 12:
24, 36, 48, 60, 72
Try 27 → reversed = 72
So the number which is reversed is 27
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