Percentage problem 2 by Dhaval Furia

Algebra Level pending

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

10 10 8 8 7 7 9 9

Dhaval Furia by Dhaval Furia , 26, India

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1 solution

In 2010 2010 ,

Since Ratio of Ramesh's salary to Rajesh's salary is 6 : 7 6:7

Let Ramesh's salary be 6 x 6x and Rajesh's salary be 7 x 7x .(Ganesh's salary is irrelevant to the context of this question)

In 2015 2015 ,

Ramesh's salary= 125 % o f 6 x = 125 100 ⋅ 6 x = 5 4 ⋅ 6 x = 15 x 2 = 7.5 x 125\% of 6x =\dfrac{125}{100}\cdot6x=\dfrac{5}{4}\cdot6x=\dfrac{15x}{2}=7.5x

Since Ratio of Ramesh's salary to Rajesh's salary is 3 : 3 = 1 : 1 3:3=1:1 ,

So Rajesh's salary in 2015 = 7.5 x 2015 = 7.5x .

Percentage Increase in salary = I n c r e a s e i n s a l a r y O r i g i n a l s a l a r y \dfrac{Increase in salary}{Original salary} ⋅ 100 % \cdot 100\%

Percentage Increase in salary = 7.5 x − 7 x 7 x ⋅ 100 % \dfrac{7.5x-7x}{7x}\cdot100\%

Percentage Increase in salary = 0.5 x 7 x ⋅ 100 % \dfrac{0.5x}{7x}\cdot100\%

Percentage Increase in salary = 50 7 % \dfrac{50}{7}\%

Percentage Increase in salary ≈ \approx 7.142857 % 7.142857\%

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