Question

# The sum of a two digit number and the number obtained by reversing the digits is 121 and the two digits differ by 3. Find the number.

A

62 or 26

B

47 or 74

C

41 or 14

D

87 or 87

Solution

## The correct option is B 47 or 74 Let the digits at the unit's place be x and the digit at the tens place be y. Then, Number = 10y + x From  first condition (10y + x) + (10x + y) = 121 ⇒ 11(x+y)= 121 ⇒ x + y = 11 and, x - y = ± 3   [ Differences of digits is 3] Thus, we have the following sets of simultaneous equations x + y = 11      . . . (1)               x - y = 3              . . . (2) x + y = 11      . . . (3)               x - y = -3              . . . (4) On solving equations (1) and (2), we get  x + y = 11 x - y = 3 ⇒ 2x = 11 + 3 ⇒ x = 7  Substituiting x = 7 in equation (1) 7 + y = 11 ⇒ y = 4 ∴ When x = 7, y = 4, we have Number = 10y + x = 10 × 4 + 7 = 47 On solving equations (3) and (4), we get  x + y = 11 x - y = -3 ⇒ 2x = 11 - 3 ⇒ x = 4  Substituiting x = 4 in equation (3) 4 + y = 11 ⇒ y = 7 ∴ When x = 4, y = 7, we have Number = 10y + x = 10 × 7 + 4 = 74 Hence, the required number is either 47 or 74 Mathematics

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