Question

Lincoln can complete a task in 12 days, Joshua can complete it in 18 days. Chris can complete the same task in x days. Chris started the task. After 3 days, Lincoln and Joshua joined. If the task is completed in 4 more days, then find the value of x.​

Answer 1

Given :- Lincoln can complete a task in 12 days, Joshua can complete it in 18 days. Chris can complete the same task in x days. Chris started the task. After 3 days, Lincoln and Joshua joined. If the task is completed in 4 more days, then find the value of x ?

A. 14.25

B. 17.28

C. 16.5

D. 15.75

Answer :-

LCM of 12 and 18 = 36 units = Let total work .

so,

→ Efficiency of Lincoln = 36/12 = 3 unit / day

→ Efficiency of Joshua = 36/18 = 2 unit / day .

then,

→ Efficiency of (Lincoln + Joshua) = 3 + 2 = 5 unit / day .

now, let efficiency of chris is x unit / day .

so,

→ Chris 3 days work + (chris + lincoln + joshua) 4 days work = total work

→ 3x + 4(5 + x) = 36

→ 3x + 4x + 20 = 36

→ 7x = 36 - 20

→ 7x = 16

→ x = (16/7) unit / day .

therefore,

→ Time taken by chris alone = 36 / (16/7) = (36 * 7)/16 = 15.75 days (Ans.D)

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Answer 2

Given : Lincoln can complete a task in 12 days,

Joshua can complete it in 18 days.

Chris can complete the same task in x days.

Chris started the task.

After 3 days, Lincoln and Joshua joined.

If the task is completed in 4 more days,

To  find : the value of x.​

Solution:

Chris started the task.

After 3 days, Lincoln and Joshua joined.

the task is completed in 4 more days,

=> Chris worked for 3 + 4 = 7 days  and  Lincoln and Joshua worked for  4 days each

Lincoln work done in 4 days  = 4 /12   = 1/3

Joshua work done in 4 days  = 4/18   = 2/9

Chris   work done in 7 days  = 7/x

Total work = 1

=> 1/3  + 2/9  + 7/x  = 1

=>   3x  + 2x  + 63  = 9x

=> 4x = 63

=> x =  63/4

=>   x = 15.75

value of x.​ = 63/4  or 15.75

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