Alligations or Mixtures
Aptitude

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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

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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*}


(3) Comment(s)


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 explanationSmile