Question

The sum of two numbers is 5000. If 20% of one is equal to 30% of the other number , find the numbers

Answer 1

$\underline{\underline{\Huge{\textbf{Solution:}}}}$

Given,
$\textit{Statement-1}$
Sum of the two numbers is 5000

$\textit{Statement-2}$
If 20% of one number is equal to 30% of other number.

$\underline{\huge{\textsf{Step-1:}}}$
Assume 2 variables for the two numbers

Let $\textbf{x}$ be one of the number
and other number be $\textbf{y}$



$\underline{\huge{\textsf{Step-2:}}}$
Rewrite statement-2

$\implies$ 20% of x = 30% of y

We have,
$\bigstar\: \mathbf{x\%\: of y = \dfrac{x}{100} \times y = \dfrac{xy}{100}}$

$\implies \dfrac{20x}{100} = \dfrac{30y}{100}$

$\implies 2x = 3y$ ————[1]



$\underline{\huge{\textsf{Step-3:}}}$
Rewrite statement-1

$\implies$ x + y = 5000 ————[2]



$\underline{\huge{\textsf{Step-4:}}}$
Multiply with [2] on both sides of eq.[2]

$\implies$ 2(x + y) = 2(5000)

$\implies$ 2x + 2y = 10000 ————[3]



$\underline{\huge{\textsf{Step-5:}}}$
Substitute [1] in [5] to get a Number

$\implies$ 3y + 2y = 10000

$\implies$ 5y = 10000

$\implies$ y = 2000



$\underline{\huge{\textsf{Step-6:}}}$
Find the other number using [1]

$\implies$ 2x = 3(2000)

$\implies$ 2x = 6000

$\implies$ x = 3000



$\underline{\LARGE{\textbf{Verification:}}}$

The Numbers are : 2000 , 3000

$\star$ 2000 + 3000 = 5000 (Statement-1 satisfied)

$\star$ 20% of 3000 = 30% of 2000

$\implies \frac{20\times3000}{100} = \frac{30\times 2000}{100}$

$\implies 20\times30 = 30\times 20$

$\implies 600 = 600$
(Statement-2 satisfied)

$\therefore$
$\blacksquare\: \textsf{The Required Numbers are \underline{\large{\textbf{3000\: , \: 2000}}}}$

Answer 2

Answer:

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