Question

If three times the larger of the two numbers is divided by the smaller
one, we get 4 as quotient and 3 as the remainder. Also if seven times
the smaller no. is divided by the larger one, we get 5 as quotient and 1
as remainder. Find ​

Answer 1

Hey mate,

Let the number be x and the smaller one will y. We know that Divided = Divisor × Quotient + Remainder.

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

When 7y is divided by x . We get 5 as Quotient and 1 as remainder.

7y = 5x + 1 => 5x - 7y + 1 = 0

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

$\frac{x}{-4 -21}$ = $\frac{-y}{3 + 15}$ = $\frac{1}{-21 +20}$

$\frac{x}{25}$ = -1 , $\frac{-y}{18}$ = -1

=> x = 25 and y = 18

Hence, The required numbers are 25 and 18.

Hope it helps...

$( Itz ❤Aakanksha❤ here! ) {}^{}$