SSC GD 2024 PYQ — Question 58

The correct answer is option 4 i.e. 200 days.

 

 The amount of work that Anil can do in one day = ( A\),

The amount of work that Karan can do in one day = ( K ),

The amount of work that Himanshu can do in one day =  ( H).

( A + K = 1 / 20) (Anil and Karan together can complete the work in 20 days),

( K + H = 1 / 25 ) (Karan and Himanshu together can complete the work in 25 days),

( H + A = 1 / 50) (Himanshu and Anil together can complete the work in 50 days).

⇒ (A + K) + (K + H) + (H + A) = $\frac{1}{20} + \frac{1}{25} + \frac{1}{50}$

⇒ 2A + 2K + 2H = $\frac{1}{20} + \frac{1}{25} + \frac{1}{50}$

⇒ 2(A + K + H) = $\frac{1}{20} + \frac{1}{25} + \frac{1}{50}$

⇒ $\frac{1}{20} + \frac{1}{25} + \frac{1}{50} = \frac{5}{100} + \frac{4}{100} + \frac{2}{100} = \frac{11}{100}$

 

⇒ Solve for $A + K + H$

⇒ 2(A + K + H) = 11 / 100

⇒ A + K + H = 11 / 200

The second equation that $( K + H = \frac{1}{25} = \frac{4}{100} = \frac{8}{200} )$

 subtract this from ( A + K + H ) to find ( A):

⇒ A + K + H - (K + H) = $\frac{11}{200} - \frac{8}{200}$

⇒ A = 3 / 200

 A = $\frac{3}{200}$ into the first equation $( A + K = \frac{1}{20} = \frac{5}{100} = \frac{10}{200} )$

⇒$\frac{3}{200} + K = \frac{10}{200}$

⇒ K = $\frac{10}{200} - \frac{3}{200} = \frac{7}{200}$

 K =$\frac{7}{200}$ into the second equation ( K + H = $\frac{8}{200}$ ):

⇒ $\frac{7}{200} + H = \frac{8}{200}$

⇒ H = $\frac{8}{200} - \frac{7}{200} = \frac{1}{200}$

Himanshu works at a rate:

⇒ $\frac{1}{\frac{1}{200}} = 200$ days