JIPMAT 2022 (QA) - A two digit number is 7 times the sum of its two digits. The number that is formed by reversing its digits is 18 less than the original number. What is the number? | PYQs + Solutions | AfterBoards
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JIPMAT 2022

Number System
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Unit Digit

Medium

A two digit number is 7 times the sum of its two digits. The number that is formed by reversing its digits is 18 less than the original number. What is the number?

Correct Option: 2
Let me solve this step by step:
Let number be abab where aa and bb are single digits.
First condition: \newline 10a+b=7(a+b)10a + b = 7(a + b)
10a+b=7a+7b10a + b = 7a + 7b
3a−6b=03a - 6b = 0
a=2ba = 2b ...(1)
Second condition: \newline Original number = 10a+b10a + b \newline Reversed number = 10b+a10b + a
(10a+b)−(10b+a)=18(10a + b) - (10b + a) = 18
9a−9b=189a - 9b = 18
a−b=2a - b = 2 ...(2)
From (1): a=2ba = 2b \newline Substituting in (2): \newline 2b−b=22b - b = 2
b=2b = 2
Therefore a=4a = 4
Number =42= 42

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