# The sum of 2 nos is 4000 . If 15 % of one is equal to 25% of the other no. Find the nos ?

Dec 2, 2016

The numbers are $x = 2500$ and $y = 1500$.

#### Explanation:

Let x and y be the two numbers.

First equation:
$x + y = 4000$

Second equation (remember 15% of a number means $.15$ times the number):
$.15 x = .25 y$

Isolate y in the first equation:
$x + y = 4000$
$y = 4000 - x$

Substitute this into the second equation:
$.15 x = .25 \left(4000 - x\right)$
Distribute and solve for x:
$.15 x = 1000 - .25 x$
$.4 x = 1000$
$x = 2500$

Substitute this into first equation written in terms of y:
$y = 4000 - x$
$y = 4000 - \left(2500\right)$
$y = 1500$

Dec 3, 2016

$a = 2500 \text{ } b = 1500$

#### Explanation:

Let one value be represented as $a$
Let the other letter be represented as $b$

Then we have $a + b = 4000$...Equation(1)

Also we have:

$\frac{15}{100} a = \frac{25}{100} b$

$\implies a = \frac{25}{\cancel{100}} \times \frac{\cancel{100}}{15} b$

$a = \frac{5}{3} b$ ......................................Equation(2)
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$\textcolor{b l u e}{\text{Determine the value of } b}$

substitute for $a$ in equation(1) using equation(2)

$a + b = 4000 \text{ "->" } \frac{5}{3} b + b = 4000$

$\frac{8}{3} b = 4000$

$b = \frac{3}{8} \times 4000$

$\textcolor{b l u e}{b = 1500}$

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$\textcolor{b l u e}{\text{Determine the value of } a}$

$\textcolor{b l u e}{a = 4000 - 1500 = 2500}$

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$\textcolor{b r o w n}{\text{Check}}$

$\frac{15}{100} a \text{ } = \frac{25}{100} b$

Consider the LHS
$\frac{15}{100} \times 2500 = 375$

Consider the RHS
$\frac{25}{100} \times 1500 = 375$

$L H S = R H S \text{ }$ so correct