Question

In his will, Rushveer Singh distributed
all his money among his 3 children.
The eldest one got Rupees 2 lakh more
than 50% of the total money, while the
younger one got Rupees 3 lakh less
than 25% of the total money. The
remaining money went to the middle
child, who bought a house with 50% of
the money he got, and was left with
Rupees 6 lakh less than what the
youngest one got. How much money
did the youngest one get ?

Answer 1

Answer 2

$Let \: the \: Total \: money\:with \:Rushveer$

$Singh = Rs \: x \: lakh\: --(1)$

$The \: amount \:of \: money \: Elder \: son$

$got = 50\% \:of \: x - 2\: lakh$

$= \frac{x}{2} +2 \: --(2)$

$The \: amount \:of \: money \: Younger \: son$

$got = 25\% \:of \: x -3 \: lakh$

$= \frac{x}{4} -3 \: --(3)$

$The \: amount \:of \: money \: middle \: child$

$got = (1) - (2) - (3)$

$= x - ( \frac{x}{2} + 2 ) - ( \frac{x}{4} - 3) \: --(4)$

/* According to the problem given */

$\frac{1}{2}\times (4) = (3) - 6 \: lakh$

$\implies \frac{1}{2} [ x - ( \frac{x}{2} + 2 ) - ( \frac{x}{4} - 3)] = ( \frac{x}{4} - 3 ) - 6$

$\implies x - \frac{x}{2} -2 - \frac{x}{4} + 3 = 2[ \frac{x}{4} - 3 - 6]$

$\implies x - \frac{x}{2} - \frac{x}{4} + 1 = \frac{x}{2} - 18$

$\implies x - \frac{x}{2} - \frac{x}{4} - \frac{x}{2}= -1 - 18$

$\implies \frac{ 4x - 2x - x-2x}{4} = - 19$

$\implies \frac{-x}{4} = -19$

$\implies x = (-19) \times (-4)$

$\implies x = 76\: --(5)$

$\red{ Amount \: of \:money \: younger \: son }$

$\red{ got }$

$= \frac{x}{4} -3$

$= \frac{76}{4} - 3$

$= 19 - 3$

$\green {= 16 \:lakh}$

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