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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

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B

47 or 74

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C

41 or 14

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D

87 or 87

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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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