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.
Answers
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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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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