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 the remainder. Find the numbers. fast

​

Answer 1

Given :-

• When 3 times the larger number is divided by the smaller number, we get 4 as quotient and 3 as the remainder.
• When 7 times the smaller number is divided by the larger number, we get 5 as quotient and 1 as remainder.

To Find :-

• The two numbers.

Solution :-

Let the larger number be x and the smaller number be y. Now, we know that,

Dividend = (Divisor × Quotient) + Remainder

A.T.Q,

When 3x is divided by y, we get 4 as quotient and 3 as remainder. Then, by using the above formula, we get,

⇒ 3x = 4y + 3

⇒ 3x - 4y = 3.....( 1 )

Again, when 7y is divided by x, we get 5 as quotient and 1 as remainder. Then, by using the above formula, we get,

⇒ 7y = 5x + 1

⇒ 5x - 7y = -1.....( 2 )

Multiplying ( 1 ) with 5 gives,

⇒ 15x - 20y = 15.....( 3 )

Multiplying ( 2 ) with 3 gives,

⇒ 15x - 21y = -3.......( 4 )

Subtracting ( 4 ) from ( 3 ), we get,

⇒ y = 18

Substituting value of y in ( 1 ) gives,

⇒ 3x - 4 × 18 = 3

⇒ 3x = 3 + 72

⇒ 3x = 75

⇒ x = 75/3

⇒ x = 25

Therefore, the required numbers are 25 and 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.

PLS MARK BRAINLIEST