Question

A man loses 20% of his money. After spending 25% of the remaining, he has ₹510 left with him.
How much money did he originally have?
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Answer 1

Given:

• A man loses 20% of his money. After spending 25% of the remaining, he has ₹510 left with him. How much money did he originally have?

AnsweR:

• ₹ 850

Solution:

Let the original amount be ₹ x

$\\ \sf \: Amount \: lost = 20 \% \: of \: ₹ \: \\ \\ \implies \sf \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: x = ₹ \bigg( \frac{20}{100} \times x \bigg)\\ \\ \sf \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = ₹ \: \frac{x}{5} \: \: \:$

$\\ \sf \: Remainder = ₹ \bigg( x - \frac{ x }{5} \bigg) \: \: = ₹ \: \frac{4x}{5}$

$\\ \sf Expenditure = 25 \% \: of \: the \: remainder \: \\ \\ \sf \: \: \: \: \: \: = 25\% \: of \: ₹ \: \frac{4x}{5} \\ \\ \sf \: \: \: \: \: \: \: \: \: \: = \: ₹ \bigg( \frac{25}{100} \times \frac{4x}{5} \bigg) \\ \\ \sf \: \: \: \: \: \: \: \: \: \: = \: ₹ \: \frac{x}{5} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:$

$\\ \sf \: Amount \: left = ₹ \: \bigg( \frac{4x}{5} - \frac{x}{5} \bigg) \\ \\ \sf \: \: \: \: \: \: \: \: = ₹ \: \frac{3x}{5}$

As per given question,

$\\ \sf \: \: \: \: \: \: \: \: \: \: \: \: \: ₹ \: \frac{3x}{5} = ₹ \: 510 \\ \\ \: \implies \sf \: \: \: \frac{3x}{5} = 510 \\ \\ \: \: \: \: \: \: \: \: \: \sf \implies \: \: \: \: \: x = \frac{510 \times 5}{3} \\ \\ \: \: \: \sf \implies \: \: \: \: \: \: x \: = ₹ \: 850$

⠀⠀⠀⠀⠀⠀Hence, the man had ₹ 850.

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⠀⠀⠀⠀⠀⠀⠀⠀Hope it helps you!!

⠀⠀⠀⠀⠀⠀Stay home! Stay Safe!!!