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Byju's Answer

Standard IX

Mathematics

Linear Equation in 2 Variables

Madhav starte...

Question

Madhav started playing a card game. In the first round, he doubled his amount and he gave away $p$ rupees to his friend. In the second round, he tripled and amount left with him after the first round and gave away $2 p$ rupees to his friend. In the third round, he quadrupled the amount left with him after the second round and gave away $p$ rupees to his friend and was finally left with no money. If he gave away a total of $R s . 160$ to his friend, then what was the amount that he started with?

R s . 21

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R s . 40

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R s . 24

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R s . 35

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Solution

The correct option is D $R s . 35$
Started gained Given to friend Lett over
$x$ $2 x$ $P$ $2 x - p$
$2 x - p$ $3 (2 x - p) = 6 x - 3 p$ $2 p$ $6 x - 5 p$
$6 x - 5 p$ $4 (6 x - 5 p) = 24 x - 20 p$ $\frac{P}{4 P}$ $24 x - 21 p = 0$
given $4 P = 160$

$P = 40$

and $24 x - 21 P = 0$

$24 \times x = 21 \times 40$

$x = 35$

$∴$ he satrted with amount = $35$

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Started	gained	Given to friend	Lett over
$x$	$2 x$	$P$	$2 x - p$
$2 x - p$	$3 (2 x - p) = 6 x - 3 p$	$2 p$	$6 x - 5 p$
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The correct option is D Rs.35 Started gained Given to friend Lett over x 2x P 2x−p 2x−p 3(2x−p)=6x−3p 2p6x−5p 6x−5p 4(6x−5p)=24x−20p P4P 24x−21p=0 given 4P=160 P=40 and 24x−21P=0 24×x=21×40 x=35 ∴ he satrted with amount = 35