Question

How many kilograms of sugar costing $Rs.9$ per kg must be mixed with $27kg$ of sugar costing $Rs.7$ per kg so that there may be gain of $10\%$ by selling the mixture at $Rs.9.24$ per kg?

• A. $36kg$
• B. $42kg$
• C. $54kg$
• D. $63kg$

Answer 1

The correct option is D $63kg$

S.P. of 1 kg of mixture = Rs. $9.24$

$\Rightarrow$ Gain of 10 $\%$

$\therefore$ C.P. of 1 kg of mixture = Rs.$(\frac{100}{110}\times 9.24)$ = Rs. $8.40$

By the rule of alligation,

$\therefore \text{Ratio of}{1}^{st}\&2^{nd}\text{kind}=14:6=7:3$

Let x kg of sugar of $1^{st}$ be mixed with 27 kg of $2^{nd}$ kind $\to$

$\therefore 7:3=x:27$

$\Rightarrow x=\frac{7\times 27}{3}=63$

Hence, 63 kg of sugar costing Rs.9 per kg must be mixed with 27 kg of sugar costing Rs.7 per kg, so that there may be gain of 10 $\%$ by selling the mixture at Rs.9.24 per kg