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Q.

The number of employees who work at Company A increased by 18% during the year 2003. During 2004, the number of employees increased by 26%. Calculate the approximate percent of the increase, to the nearest percent, in employment over the two-year period.

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a

31%

b

44%

c

49%

d

53%

answer is C.

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Detailed Solution

Concept- First, we will assume the original no. of employees to be x. And then, we will use the general formula of percentage that we studied in the chapter . i.e.

(Percentage increase = \frac{change in quantity}{Original quantity} \times 100 %)

Given: In company A, Number of employees increased by 18% in 2003
Number of employees increased by 26% in 2004
Assume the original no. of employees to be x and the x’ in the year 2003 after increase
In 2003, there was 18% increase,
thus, by using the required formula of percentage increase

Percentage increase = \frac{change in quantity}{Original quantity} \times 100 %

Now, substitute the values in the formula

\Rightarrow 18 = \frac{x' - x}{x} \times 100 %

\Rightarrow 0.18 x = x' - x

\Rightarrow 0.18 x + x = x'

\Rightarrow 1.18 x = x'

-(i)
Similarly, we will do for the no. of employees in 2004
Assume the no. of employees to be y and there was 26% increase

\Rightarrow 26 = \frac{y - x'}{x'} \times 100 %

\Rightarrow 0.26 x' = y - x'

\Rightarrow 0.26 x^{'} + x' = y

\Rightarrow 0.26 x' = y

-(ii)
Substitute the values of eq.(i) in eq.(ii)
From (i) , we get

\Rightarrow 1.18 x = x'

\Rightarrow 0.26 x^{'} = y \Rightarrow 0.26 (1.18 x) = y

\Rightarrow y = 1.4868 x

Now, calculate the percentage increase

Percentage increase = \frac{y - x}{x} \times 100 %

\Rightarrow \frac{1.4868 x - x}{x} \times 100 %

\Rightarrow 48.68 %

Percentage increase in the no. of employees= 48.68 %
The nearest value is 49%.
Hence, the correct option is (3) .

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