# Moderate Alligations or Mixtures Solved QuestionAptitude Discussion

 Q. 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. 60 kg ✔ B. 63 kg ✖ C. 50 kg ✖ D. 77 kg

Solution:
Option(B) is correct

Let the rate of second quality be Rs $x$ per Kg.

C.P of 1 Kg sugar of 1st 980p

Step 1 :

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

Gain = 10%

C.P of 1 kg of mixture $=\left[\dfrac{100}{100+10}\times 9.24\right]$

$=\text{Rs. } 8.40$

$\Rightarrow$ Mean price = Rs. 8.40

Step 2 :

C.P of  1 kg of sugar of  1st kind = 900p

C.P of  1 kg of sugar of  2nd kind = 700p

Mean price = 840p

By the rule of alligation, we have:

C.P. of 1kg of                    C.P. of 1kg of

sugar of 1st                      sugar of 2nd

kind (900p)                       kind (700p)

\                    /

Mean Price
(840p)

/                    \

840 - 700          :            900 - 840

(140)                                (60)

⇒Required ratio $= 140 : 60 = 7 : 3$

Step 3:

Let $x$ kg of sugar of 1st kind be mixed with 27 kg of 2nd kind

\begin{align*}
7:3&=x:27\\
\Rightarrow \dfrac{7}{3}&=\dfrac{x}{27}\\
\Rightarrow x &= \left(\dfrac{7}{3}\times 27\right)\\
&=63 \text{ Kg.}
\end{align*}

## (4) Comment(s)

Naredra
()

hi we can find the ratio of quantity by putting 7 rs/kg and 9rs/kg and mean price of rs,8.40/kg

Chandler Monica
()

Simpler solution could be, its given as 27kg of 7rs Sugar.. so obviously 100-27 = 63kg remaining should be of 9rs Sugar..

Simple ryt??

Priyanka
()

HI Monica,

100-27 =73.

Shekhar
()

very very good explanation

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