Question

12. A number When divided by a divisor leaves a remainder of 24 years. When twice the original number is divided by the same divisor, the reminder is 11. What is the value of the divisor?

Answer 1

Given :

A number When divided by a divisor leaves a remainder of 24 years. When twice the original number is divided by the same divisor, the reminder is 11.

To find :

value of the divisor

Solution :

let the divisor by x and quotient be y

then number = xy + 24

twice the number

= 2xy + 48

now 2xy is completely divisible by y

on dividing 48 by x remainder is 11

x = 48 - 11

x = 37

=> value of divisor by 37

Answer 2

Given:-

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• A number When divided by a divisor leaves a remainder of 24 years. When twice the original number is divided by the same divisor, the reminder is 11.

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To Find:-

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• What is the value of the divisor?

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STEP BY STEP EXPLANATION:-

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$\bf x = m.n + 24 \\ \\ \\ \bf2x = m.p + 11 \\ \\ \\ \bf \implies mp + 11= 2mn + 48 \\ \\ \\ \bf \implies mp = 2mn + 37\\ \\ \\ \bf \implies m(p - 2n) = 37 \\ \\ \\ \bf \therefore m = \frac{37}{p - 2n} \\ \\ \\ \bf \therefore \: 37 \: is \: prime \: number \: and \: m \: is \: integers \\ \\ \\ \bf \therefore m = 37 \: or \: 1 \\ \\ \\ \bf \therefore m = 37$