Question

A number is 9/17 of another number. On adding the larger number and three times the smaller number, the sum obtained is 9284. The two numbers are ___ and ___.

Answer 1

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Let the larger number be x and the smaller one be y. We know that

Dividend =(Divisor × Quotient) +Remainder. (i)

When 3x is divided by y, we get 4 as quotient and 3 as remainder. Therefore, by using (i), we get

3x=4y+3⇒3x−4y−3=0 (ii)

When 7y is divided by x, we get 5 as quotient and 1 as remainder. Therefore, by using (i), we get

7y=5x+1⇒5x−7y+1=0 .(iii)

Solving equations (ii) and (iii), by cross-multiplication, we get

−4−21x=3+15−y=−21+201

−25x=−1, 18−y=−1

⇒x=25 and y=18

Hence, the required numbers are 25 and 18