If three times the larger of two numbers is divided by the smaller, we get 4 as the quotient and 8 as the remainder. If five times the smaller is divided by the larger, we get 3 as the quotient and 5 as the remainder. Find the numbers.

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Rajan@2021Guru

Asked: April 27, 20212021-04-27T07:33:33+05:30 2021-04-27T07:33:33+05:30In: CBSE

If three times the larger of two numbers is divided by the smaller, we get 4 as the quotient and 8 as the remainder. If five times the smaller is divided by the larger, we get 3 as the quotient and 5 as the remainder. Find the numbers.

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One of the most important and conceptual question from linear equations in two variables in which we have to find the numbers if three times the larger of two numbers is divided by the smaller, we get 4 as the quotient and 8 as the remainder. If five times the smaller is divided by the larger, we get 3 as the quotient and 5 as the remainder.

RS Aggarwal, Class10, chapter 3E, question no 8

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MathsMentor · Answer 1 · 2021-04-27T09:34:21+05:30

MathsMentor Guru

2021-04-27T09:34:21+05:30Added an answer on April 27, 2021 at 9:34 am

Let the larger number be x and the smaller number be y.

Then, according to the question.
3x=4y+8
3x−4y=8 …….(1)
And, 5y=3x+5
3x−5y=−5 …..(2)
Solving equation 1 and 2, we get,
x=20 and y=13
Therefore, the required numbers are 20 and 13.