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Solving Linear Equations Using Transpose of Terms

If three time...

Question

If three times the larger of two number is divided by the smaller, the quotient and the remainder, each is equal to 6. If five times the smaller is divided by the larger, the quotient is 2 and the remainder is 3. The smaller number is

A

6

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B

7

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C

8

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D

9

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Solution

The correct option is B $7$
Let the larger number be L and smaller be S,
$3 L = 6 S + 6$
and, $5 S = 2 L + 3$
Multiply equation (1) by 2 and equation(2) by 3 and add
$15 S - 12 S = 12 + 9$
$S = 7$
Thus , the smaller number is $7$

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