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CAT 2019 Slot 2 — QA Question 23

Percentage ChangeEasy

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

Answer & solution

Correct answer: 7

  • 7

  • B

    8

  • C

    9

  • D

    10

Solution

Easy

Assign one scale variable to each year's ratio. Ramesh's known 25%25\% rise links the two scales; then read off Rajesh's 2010 and 2015 salaries in a common variable and compute the percentage change.

1

Set up both years. In 2010, salaries are 6x,5x,7x6x,5x,7x (Ramesh, Ganesh, Rajesh). In 2015 they are 3y,4y,3y3y,4y,3y.

2010: R=6x, G=5x, Raj=7x2015: R=3y, G=4y, Raj=3y\begin{aligned} &2010:\ R{=}6x,\ G{=}5x,\ \text{Raj}{=}7x\\ &2015:\ R{=}3y,\ G{=}4y,\ \text{Raj}{=}3y \end{aligned}
2

Use Ramesh's 25%25\% rise. Ramesh's 2015 salary is 1.251.25 times his 2010 salary.

3y=54×6x⇒ 3y=7.5x ⇒ y=2.5x\begin{aligned} &3y=\frac{5}{4}\times 6x\\ &\Rightarrow\ 3y=7.5x\ \Rightarrow\ y=2.5x \end{aligned}
3

Rajesh's percentage increase. Rajesh: 7x7x in 2010 and 3y=3(2.5x)=7.5x3y=3(2.5x)=7.5x in 2015.

increase=7.5x−7x7x×100%⇒ =0.57×100%≈7.14%≈7%\begin{aligned} &\text{increase}=\frac{7.5x-7x}{7x}\times 100\%\\ &\Rightarrow\ =\frac{0.5}{7}\times 100\%\approx 7.14\%\approx 7\% \end{aligned}
Closest to 7%\text{Closest to }7\%

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CAT 2019 Slot 2 QA Q23: The salaries of Ramesh, Ganesh and Rajesh were in the ratio 6 : 5 : 7 in 2010, and in the ratio 3 : 4 : 3 in 2 — Solution | TheCATExam