Alligations or Mixtures
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Q.

Weights of two friends Ram and Shyam are in the ratio 4:5.

If Ram's weight is increased by 10% and total weight of Ram and Shyam become 82.8 kg, with an increases of 15%, by what percent did the weight of Shyam has to be increased?

 A.

17%

 B.

19%

 C.

23%

 D.

29%

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Solution:
Option(B) is correct

Let, Shyam's weight, $S$ has been increased by $x\%$.

and as per the question Ram's weight, $R$ is increased by 10%,

Ram $(R)$               Shyam $(S)$
$(10\%)$                     $(x\%)$
         \                      /
               mean
             $(15\%)$
         /                    \
$(x-15)\%$      :     $(15-10)\%$

Now, given ratio of Ram and Shayam's weight,

$\dfrac{R}{S}= \dfrac{4}{5}$

$\Rightarrow \dfrac{x-15}{15-10} = \dfrac{4}{5}$

$\Rightarrow \textbf{x = 19%}$


(3) Comment(s)


Deepak
 ()

Ration is given for initial weight, not for resultant weight after increasing



Akshaya
 ()

10% is the increase in percentage weight of ram. What does (x-15)% denote?


Deepak
 ()

This is the difference between the desired and current values. This is a standard step used in the Alligation technique.

You can learn more about it in the Alligation Introduction Section.