Question

Sum of two integers is 87. If greater integer is divided by smaller, the quotient is 4 and remainder is 12.Find the numbers​

Answer 1

Answer:

75 i hope you understand

Answer 2

The two numbers are 72 and 15.

Given,

The sum of two integers = 87,

Quotient and remainder when greater integer divided by smaller = 4 and 12 respectively.

To find,

The numbers.

Solution,

Let the two integers be $x$ and $y$, such that $x > y$.

It is given that their sum is 87.

$\implies x+y=87$     ...(1)

Now, if we divide a number (dividend) by another (divisor), we have the relation,

$dividend(D)=quotient (q) \times divisor (d)+ remainder (r)$     ...(2)

Here, as $x$ is assumed greater, we have to divide $x$ by $y$. So,

$D = x, and,\\d=y$

It is given that,

$q=4,\\r=12$.

Substituting in equation (2),

$x=4 \times y+12\\\implies x=4y+12$     ...(3)

From eq. (1), substituting $y=87-x$ in above eq. (3), we get,

$x=4(87-x)+12$

Simplifying,

$x=348-4x+12$

$\implies 5x=360$

⇒ x = 72.

Since from (1),

$y=87-x$

$\implies y=87-72$

⇒ y = 15.

⇒ the two numbers = 72, 15.

Therefore, the two numbers are 72 and 15.