A certain number of men can complete a piece of work in 6k days

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Question 1: –  A certain number of men can complete a piece of work in 6k days, where k is natural number. By what percent should the number of men be increased so that the work can be completed in 5k days ?             [UPSC CSAT 2024]

A). 10%           B). (50/3)%

C). 20%           D).  25%

Solution:-  Let the number of men in first case = M_1

And number of days in first case = D_1

The number of men in second case = M_2

And number of days in second case = D_2

Let number of worker M_1 = x

D_1 = 6k, D_2 = 5k

Now, from formula

Number of workers in first case × Number of days in first case = Number of workers in second case × Number of days in second case

M_1 \times D_1 = M_2 \times D_2

x \times 6k = M_2 \times 5k

⇒ M_2 = \dfrac{6x}{5}

Change in workers = \dfrac{6x}{5} - x

= x/5

Percentage change in workers to complete their work in 5k days

=\dfrac{x/5 \times 100}{x} = 20%

Answer:- Option (C) 20%

Some other question

Question:- X Y and Z can complete a piece of work individually in 6 hours 8 hours and 8 hours respectively. However, only one person at a time can work in each hour and nobody can work for two consecutive hours. All are engaged to finish the work. What is the minimum amount of time that they will take to finish the work ?                   {UPSC CSAT 2024]

Solution:- See full solution

  1.  Find nth derivative of the function 1+x/1-x

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