Q) The sum of the digits of a 2-digit number is 14. The number obtained by interchanging its digits exceeds the given number by 18. Find the number.

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

Hence the given number is 10 X + Y

∴ the sum of the digits = X + Y

By 1st given condition: X + Y = 14 ………… (i)

Next, by other given condition, when digits are interchanged, new number exceeds the given number by 18

∴ we will get new number as: 10 Y + X

∴ (10 Y + X) – (10 X + Y) = 18

∴ 9 Y – 9 X = 18

∴ Y – X = 2 …………… (ii)

Next, by adding equations (i) and (ii), we get:

(X + Y) + (Y – X) = 14 + 2

∴ 2 Y = 16

∴ Y = = 8

by transferring Y = 8 in equation (ii), we get:

Y – X = 2

(8) – X = 2

∴ X = 8 – 2 = 6

Hence, the original number:  10 X + Y = 10 (6) + 8 = 68.

Therefore, the given number is 68.

Check:

1) Sum of the digits is 6 + 8 = 14

2) When we interchange the digits, new number is 86 and 86 is larger from 68 by (86 – 68) = 18 

Hence our solution is correct.

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