Siddharth, Nikita, Vinay and Neha individually takes different number of hours to complete a task. If Siddharth, Nikita and Vinay works together then they take 6 hours 40 minutes to complete the task and if Nikita, Vinay and Neha works together then they take 8 hours to complete the task. If Siddharth and Neha working together complete the task in 13 hours 20 minutes, then how much time will all the four persons take to complete the task working together?

Question

cdquestions Admin · Accepted Answer

Let the number of hours taken by Siddharth to complete the task = S Work done by Siddharth in 1 hour = ( $\frac{1}{S}$ ) Let the number of hours taken by Nikita to complete the task = N Work done by Nikita in 1 hour = ( $\frac{1}{N}$ ) Let the number of hours taken by Vinay to complete the task = V Work done by Vinay in 1 hour = ( $\frac{1}{V}$ ) Let the number of hours taken by Neha to complete the task = T Work done by Neha in 1 hour = ( $\frac{1}{T}$ ) Siddharth, Nikita and Vinay take 6 hours 40 minutes to complete the task = 6 ( $\frac{40}{60}$ ) = $\frac{20}{3}$  hrs Work done by Siddharth, Nikita and Vinay in 1 hour = 3/20 ( $\frac{1}{S}$ ) + ( $\frac{1}{N}$ ) + ( $\frac{1}{V}$ ) = ( $\frac{3}{20}$ ).............................................. (1) Nikita, Vinay and Neha take 8 hours to complete the task Work done by Nikita, Vinay and Neha in 1 hour = 1/8 ( $\frac{1}{V}$ ) + ( $\frac{1}{V}$ ) + ( $\frac{1}{T}$ ) = ( $\frac{1}{8}$ ).............................................. (2) Subtracting (2) from (1) we get ( $\frac{1}{S}$ ) - ( $\frac{1}{T}$ ) = ( $\frac{3}{20}$ ) - ( $\frac{1}{8}$ ) ( $\frac{1}{S}$ ) - ( $\frac{1}{T}$ ) = ( $\frac{1}{40}$ )................................. (3) Also, Siddharth and Neha take 13 hours 20 minutes to complete the task = 13 ( $\frac{20}{60}$ ) = ( $\frac{40}{3}$ ) hours Work done by Siddharth and Neha in 1 hour = (3/40) ( $\frac{1}{S}$ ) + ( $\frac{1}{T}$ ) = ( $\frac{3}{40}$ ).................................. (4) Adding (3) and (4) we get 2 x ( $\frac{1}{S}$ ) = ( $\frac{4}{40}$ ) ( $\frac{1}{S}$ ) =  $\frac{1}{20}$ Substituting in equation 4 we get ( $\frac{1}{T}$ ) = ( $\frac{3}{40}$ ) - ( $\frac{1}{20}$ ) = ( $\frac{1}{40}$ ) Total work done by all four persons together = ( $\frac{1}{S}$ ) + ( $\frac{1}{N}$ ) + ( $\frac{1}{V}$ ) +( $\frac{1}{T}$ ) = ( $\frac{3}{20}$ ) + ( $\frac{1}{40}$ ) = ( $\frac{7}{40}$ ) Total number of hours required = ( $\frac{40}{7}$ ) = 5 ( $\frac{5}{7}$ ) hours.

Answer

4($\frac{4}{7}$) hours.

Answer

5($\frac{3}{7}$) hours.

Answer

5($\frac{5}{7}$) hours.

Answer

6($\frac{5}{7}$) hours.

Answer

5($\frac{2}{3}$) hours.

The Correct Option is C

Solution and Explanation

Top Questions on Time Speed and Distance

Questions Asked in CAT exam