Question

Two whole numbers are given. If three times larger number is divided by smaller number,then 4 as a quotient and 3 as a remainder are obtained. If seven times of smaller number is divided by larger number, then 5 as quotient and 1 as a reminder are obtained. smaller number is equal to??? ​

Answer 1

Answer:

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

−4−21

x

=

3+15

−y

=

−21+20

1

−25

x

=−1,

18

−y

=−1

⇒x=25 and y=18

Answer 2

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

−4−21

x

=

3+15

−y

=

−21+20

1

−25

x

=−1,

18

−y

=−1

⇒x=25 and y=18

Hence, the required numbers are 25 and 18.

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