If three times the larger of the two numbers is divided by the smaller one, we get 4 as quotient - Maths -

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 number is divided by the
larger one, we get 5 as quotient and 1 as remainder Find the
numbers

Ajanta Trivedi · Accepted Answer

let the larger number be x and the smaller number be y.

3 times of the larger number = 3x

As dividend = divisor * quotient + remainder

since if the three times of the larger number is divided by the smaller number,

quotient = 4 and remainder = 3

$3 x = 4 y + 3 3 x - 4 y = 3............ (1)$

if 7 times the smaller number is divided by the larger one , quotient =5 and remainder =1

$7 y = 5 x + 1 - 5 x + 7 y = 1...... (2)$

multiply (1) by 5 and (2) by 3 and adding,

$15 x - 20 y = 15 - 15 x + 21 y = 3 y = 18$

substtitue y=18 in (1):

$3 x - 4 * 18 = 3 3 x - 72 = 3 3 x = 3 + 72 = 75 x = \frac{75}{3} = 25$

thus the numbers are 18 and 25.

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 number is divided by the larger one, we get 5 as quotient and 1 as remainder. Find the numbers.