Q) A 2-digit number is seven times the sum of its digits. The number formed by reversing the digits is 18 less than the given number. Find the given number.

Ans: Let’s consider X and Y are the digits of the given number.

Hence the given number is 10 X + Y

Also given that Number is 7 times of the sum of the digits,

∴ (10 X + Y)  = 7 ( X + Y)

∴ 10 X + Y  = 7 X + 7 Y

∴ 3 X = 6 Y

∴ X = 2 Y ……….. (i)

Next, by reversing the digits, we will get new number as: 10 Y + X

Given that the new number is 18 less than the original number, therefore:

∴ (10 X + Y) – (10 Y + X) =  18

∴ 10 X + Y  – 10 Y – X = 18

∴ 9 X – 9 Y = 18

∴ X – Y = 2 …………… (ii)

Next, let’s solve the equations (i) & (ii), we get:

X = 4 and Y = 2.

Hence, the original number:  10 X + Y = 10 (4) + 2 = 42.

Therefore, the given number is 42.

Check:

1) Sum of the digits is 4 + 2 = 6 and 42 is 7 times of 6.

2) By reversing the digits, we get new number as 24 and it is 18 less than the original number 42.

Hence our solution is correct.

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