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If three times the larger of the two num...

If three times the larger of the two numbers is divided by the smaller one, we get 4 as quotient and 3 as remainder. Also if seven times the smaller number is divided by the larger one, we get 5 as quotient and 1 as remainder . Find the numbers.

Text Solution

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Let the larger number be x and the smaller one by y .
We know that
dividend = ( divisor ` xx` quotient ) + remainder
Using the above result and the given conditions, we have
` 3 x = 4y + 3 rArr 3 x - 4y = 3 " " `... (i)
and ` 7y = 5 x + 1 rArr 5 x - 7y = - 1 " " `... (ii)
Multiplying (i) by 5, (ii) by 3 and subtracting, we get ` y = 18`
Putting `y = 18 ` in (i), we get
` 3 x - ( 4 xx 18) = 3 rArr 3x - 72 = 3 `
`rArr 3x = 75 rArr x = 25 `
Hence, the required numbers are 25 and 18.
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