Question

A man donated 5% of his income to a charitable organisation and deposited 20% of the remainder in a bank. He has 1919 now! find his actual salary..

Answer 1

Hello!

Let his income be $\bf{x}$.

ATQ,

$\bf{x} \sf \:x\: \dfrac{\sf 100-5}{\sf 100} \sf \:x\: \dfrac{\sf 100-20}{\sf 100} = \sf 1919$

⇒ $\bf{x} \sf \:x\: \dfrac{\sf 95}{\sf 100} \sf \:x\: \dfrac{\sf 80}{\sf 100} = \sf 1919$

⇒ $\bf{x} \sf \:x\: \sf 0.95 \sf \:x\: \sf 0.80 = \sf 1919$

⇒ $\bf{x} \sf \:x\: \sf 0.76 = \sf 1919$

⇒ $\bf{x} = \dfrac{\sf 1919}{\sf 0.76} = \boxed{\sf 2525}$

Hence,
The man's income is $\bf{Rs.\: 2525}$

Cheers!

Answer 2

$\bf{\underline{ANSWER}}$

Let the man's salary be x

% of his income donated = 5%

$amount \: of \: money \: donated \: = \\ \\ = > \frac{percent \: of \: income \: donated}{100} \times \: actual \: income \\ \\ = > \frac{5}{100} \times x \\ \\ = > \frac{1}{20} x \\ \\ remaining \: income \: = \\ actual \: income \: - \: amount \: of \: money \: donated \\ \\ = > x - \frac{1}{20} x \\ \\ = > \frac{20x - x}{20} \\ \\ = > \frac{19}{20} x$

Percent of money deposited in bank = 20%

$amount \: of \: money \: deposited \: = \\ \\ = > \frac{\% \: of \: money \: deposited}{100} \times remaining \: amount \\ \\ = > \frac{20}{100} \times \frac{19}{20} x \\ \\ = > \frac{19}{100} x \\ \\ left \: over \: income \: = \\ remaining \: amount \: - \: deposited \: amount \\ \\ = > \frac{19}{20} x - \frac{19}{100} x \\ \\ = > \frac{95x - 19x}{100} \\ \\ = > \frac{76}{100} x$

GIVEN, the left over income is ₹1919

Therefore,

$\bf{\underline{THE \: EQUATION \: FORMED}}$

$\frac{76}{100} x = 1919 \\ \\ = > x = 1919 \times \frac{100}{76} \\ \\ = > \: 2525$

$\bf{\underline{ANS}}$

The actual salary of the man is ₹ $\bf{\underline{ 2525}}$

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