A number when divided by a divisor leaves a remainder of 24. When twice the original number is divided by the same divisor, the remainder is 13. What is the value of the divisor?

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Question

This question was previously asked in

SSC Selection Post 2024 (Matriculation Level) Official Paper (Held On: 25 Jun, 2024 Shift 1)

Answer 1

Given:

A number when divided by a divisor leaves a remainder of 24. When twice the original number is divided by the same divisor, the remainder is 13.

Formula used:

Let the number be N and the divisor be D.

N = kD + 24 (where k is an integer)

2N = mD + 13 (where m is an integer)

Calculation:

N = kD + 24

⇒ 2N = 2(kD + 24)

⇒ 2N = 2kD + 48

Given, 2N = mD + 13

⇒ 2kD + 48 = mD + 13

⇒ 2kD - mD = 13 - 48

⇒ D(2k - m) = -35

⇒ D = 35 (since D must be positive)

∴ The correct answer is option 1.

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