How many kg of salt at 42 P per kg must a man | vedclass

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(A) Let the cost price $(CP)$ of the mixture be $x$ $P$ per $kg$.Given that the selling price $(SP)$ is $40$ $P$ per $kg$ and the gain is $25 \%$.$CP

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$20$

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(A) Let the cost price $(CP)$ of the mixture be $x$ $P$ per $kg$.Given that the selling price $(SP)$ is $40$ $P$ per $kg$ and the gain is $25 \%$.$CP = \frac{100}{100 + 	ext{Gain } \%} 	imes SP = \frac{100}{125} 	imes 40 = \frac{4}{5} 	imes 40 = 32$ $P$ per $kg$.Using the method of alligation:Cost of first salt = $42$ $P/kg$Cost of second salt = $24$ $P/kg$Mean price = $32$ $P/kg$Difference for first salt = $|32 - 24| = 8$Difference for second salt = $|42 - 32| = 10$Ratio of quantities = $8 : 10 = 4 : 5$.Let the quantity of the first salt be $x$ $kg$.Then,$\frac{x}{25} = \frac{4}{5}$.$x = \frac{4}{5} 	imes 25 = 20$ $kg$.

How many $kg$ of salt at $42$ $P$ per $kg$ must a man mix with $25 \, kg$ of salt at $24$ $P$ per $kg$,so that he may,on selling the mixture at $40$ $P$ per $kg$,gain $25 \%$ on the outlay?

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