A ,B and C can finish a task in 42 days, 84 days and 28 days .A started the work ,B joined them after 3 days, if C joined them after 52 days from beginning ,then for how many days did A work till the completion
Answers
Let the task be x
A can finish a task in 42 days
Task done by A in 1 day = x / 42
B can finish a task in 84 days
Task done by B in 1 day = x / 84
C can finish a task in 28 days
Task done by C in 1 day = x/28
Now
According to question
A started the work ,B joined them after 3 days,
(x/42) × 3 = x / 14. – (1)
if C joined them after 52 days from beginning. This means A and B together did the work for 52– 3 days = 49 days
[ ( x / 42 ) + ( x / 84 ) ] × 49
= [ ( 2x + x) / 84 ] × 49
= ( 3x / 84 ) ×49
= (49 x / 28)
= 7x / 4 – ( 2 )
Now let the no of remaining days be y
In this remaining days all of them did the work collectively.
Hence,
( x/ 42 + x/84 + x/28 ) × y
= [ ( 2x + x + 3x) / 84 ] × y
= [ 6x / 84 ] × y
= x/14 × y
= xy/14. – ( 3 )
Adding 1, 2 amd 3
( x / 14 ) + ( 7x / 4 ) + ( xy / 14 ) = x
{Since total work is x }
( 1/14 + 7/4 + y/14 ) = 1
2+49+2y = 1 × 28
51 +2y = 28
2y = 28 – 51
Sorry my answer is coming wrong but i think this should be the approach.
Sorry once again :(