Question

The difference of two positive numbers is 72 and their quotient obtained on
dividing one by the other is 4. Find the numbers.​

Answer 1

ANSWER :-

Two numbers are 96, 24

EXPLANATION :-

Given :- Difference of two positive numbers = 72

Quotient of two positive numbers when diveded by one by other = 4

To find :- Numbers

Solution :-

Let the two positive numbers be x and y

Difference of two positive numbers = 72

⇒ x - y = 72 ---(1)

⇒ x = 72 + y ----(2)

Quotient of two positive numbers when diveded one by other = 4

We know that Dividend = (Divisor * Quotient) + Remainder

Here Divisor = y

Quotient = 4

Dividend = x

Remainder = 0 (As it is completey dividing)

⇒ x = (y * 4) + 0

⇒ x = 4y

⇒ 72 + y = 4y

[From (2)]

⇒ 72 + y = 4y

⇒ 72 = 4y - y

⇒ 72 = 3y

⇒ 72/3 = y

⇒ 24 = y

⇒ y = 24

To find the value of x substitute value of y in 1

x = 72 + y

⇒ x = 72 + 24

⇒ x = 96

$\Huge{\boxed{ \tt x = 96, \: y = 24 }}$

So two numbers are 96, 24 respectively.

VERIFICATION :-

First check with (1)

x - y = 72

⇒ 96 - 24 = 72

⇒ 72 = 72

Check with (3)

x/y = 4

⇒ 96/72 = 4

⇒ 4 = 4