Question

5. If three times, the greater of two numbers is divided by the lesser, we get the quotient 6 and the remainder 6. If 5 times the lesser number is divided by the greater, we get the quotient 2 and remainder 3. Find the two numbers.​

Answer 1

Explanation:

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 = y/3+15

=

1/−21+20

−25x =−1, 18−y =−1

⇒x=25 and y=18

Hence, the required numbers are 25 and 18.