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CAT 2019 Set-2 | Question: 67

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The salaries of Ramesh, Ganesh and Rajesh were in the ratio $6:5:7$ in $2010$, and in the ratio $3:4:3$ in $2015$. If Ramesh’s salary increased by $25\%$ during $2010-2015$, then the percentage increase in Rajesh’s salary during this period is closest to

  1. $8$
  2. $7$
  3. $9$
  4. $10$
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Ans is option (B)

Let the salaries of Ramesh, Ganesh and Rajesh in the year 2010 be : $6x,5x,7x$ respectively.

Let the salaries of Ramesh, Ganesh and Rajesh in the year 2015 be : $3y,4y,3y$ respectively.

Given that Ramesh’s salary increased by $25$%, we get this equation:

$3y=6x+\frac{1}{4}(6x)$    $\Rightarrow$  $y=\frac{5}{2}x$

Now, Rajesh’s salary in the year 2015 is : $3y=3\times\frac{5}{2}x=\frac{15x}{2}=7.5x$

$\therefore$  Pecentage increase in Rajesh’s Salary $=$  $\frac{7.5x-7x}{7x}\times100=\frac{100}{14}=7.142$%

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