Time and Work
- If A and B together can complete a work in 18 days, A and C together in 12 days and B and C together in 9 days, then B alone can do the work in
-
View Hint View Answer Discuss in Forum
(A + B)’s 1 day’s work = 1 18
(B + C)’s 1 day’s work = 1 9 (A + C)’s 1 day’s work = 1 12
Adding all the above three,2 (A + B + C)’s 1 day’s work = 1 + 1 + 1 18 9 12 2 (A + B + C)’s 1 day’s work = 2 + 4 + 3 36 2 (A + B + C)’s 1 day’s work = 9 = 1 36 4 ∴ (A + B + C)’s 1 day’s work = 1 8
∴ B’s 1 day’s work = (A + B + C)’s 1 day’s work – (A + C)’s 1 day’s workB’s 1 day’s work = 1 - 1 8 12 B’s 1 day’s work = 3 - 2 = 1 24 24
Hence, B alone can do the work in 24 days.
Second method to solve this question ,
Here , x = 18 , y = 9 , z = 12
Correct Option: B
(A + B)’s 1 day’s work = 1 18
(B + C)’s 1 day’s work = 1 9 (A + C)’s 1 day’s work = 1 12
Adding all the above three,2 (A + B + C)’s 1 day’s work = 1 + 1 + 1 18 9 12 2 (A + B + C)’s 1 day’s work = 2 + 4 + 3 36 2 (A + B + C)’s 1 day’s work = 9 = 1 36 4 ∴ (A + B + C)’s 1 day’s work = 1 8
∴ B’s 1 day’s work = (A + B + C)’s 1 day’s work – (A + C)’s 1 day’s workB’s 1 day’s work = 1 - 1 8 12 B’s 1 day’s work = 3 - 2 = 1 24 24
Hence, B alone can do the work in 24 days.
Second method to solve this question ,
Here , x = 18 , y = 9 , z = 12Time taken = 2xyz - xy + yz + zx B alone can do in = 2 × 18 × 9 × 12 - 18 × 9 + 12 × 9 + 12 × 18 B alone can do in = 36 × 108 - 162 + 108 + 216 B alone can do in = 36 × 108 = 24 days 162
- While working 7 hours a day, A alone can complete a piece of work in 6 days and B alone in 8 days. In what time would they complete it together, working 8 hours a day ?
-
View Hint View Answer Discuss in Forum
A alone can complete the work in 42 days working 1 hour daily. Similarly, B will take 56 days working 1 hour daily.
A ’s 1 day’s work = 1 42 B ’s 1 day’s work = 1 56 (A + B) ’s 1 day’s work = 1 + 1 42 56 = 4 + 3 = 7 168 168 ∴ Time taken by (A + B) working 8 hours daily = 168 = 3 days 7 × 8
Second method to solve this question ,
Here, h1 = 6 hours, h2 = 8 hours
d1 = 6 days, d2 = 8 days,
h = 8 hours
Correct Option: A
A alone can complete the work in 42 days working 1 hour daily. Similarly, B will take 56 days working 1 hour daily.
A ’s 1 day’s work = 1 42 B ’s 1 day’s work = 1 56 (A + B) ’s 1 day’s work = 1 + 1 42 56 = 4 + 3 = 7 168 168 ∴ Time taken by (A + B) working 8 hours daily = 168 = 3 days 7 × 8
Second method to solve this question ,
Here, h1 = 6 hours, h2 = 8 hours
d1 = 6 days, d2 = 8 days,
h = 8 hoursRequired Time = 
(6 ×6 ) × (8 × 8) 
× 1 6 × 6 + 8 × 8 8 Required Time = 36 × 64 × 1 100 8 Required Time = 36 × 8 = 2.88 ≈ 3 days 100 × 8
- A and B can do a piece of work in 10 days. B and C can do it in 12 days. C and A in 15 days. In how many days will C finish it alone ?
-
View Hint View Answer Discuss in Forum
(A + B)'s 1 day's work = 1 ................. (i) 10 (B + C)'s 1 day’s work = 1 ................. (ii) 12 (C + A)’s 1 day’s work = 1 ................. (iii) 15
On adding all these,2(A + B + C)’s 1 day’s work = 1 + 1 + 1 10 12 15 2(A + B + C)’s 1 day’s work = 6 + 5 + 4 = 1 60 4 ∴ (A + B + C)’s 1 day’s work = 1 ................. (iv) 8 ∴ C’s 1 day’s work = 1 - 1 8 10 C’s 1 day’s work = 5 - 4 = 1 40 40
∴ C will finish the work in 40 days.
Second method to solve this question ,
Here , x = 10 , y = 12 , z = 15Time taken = 2xyz xy - yz + zx
Correct Option: C
(A + B)'s 1 day's work = 1 ................. (i) 10 (B + C)'s 1 day’s work = 1 ................. (ii) 12 (C + A)’s 1 day’s work = 1 ................. (iii) 15
On adding all these,2(A + B + C)’s 1 day’s work = 1 + 1 + 1 10 12 15 2(A + B + C)’s 1 day’s work = 6 + 5 + 4 = 1 60 4 ∴ (A + B + C)’s 1 day’s work = 1 ................. (iv) 8 ∴ C’s 1 day’s work = 1 - 1 8 10 C’s 1 day’s work = 5 - 4 = 1 40 40
∴ C will finish the work in 40 days.
Second method to solve this question ,
Here , x = 10 , y = 12 , z = 15Time taken = 2xyz xy - yz + zx C alone can do in = 2 × 10 × 12 × 15 10 × 12 - 12 × 15 + 10 × 15 C alone can do in = 240 × 15 120 - 180 + 150 C alone can do in = 240 × 15 = 40 days 90
- If A and B together can complete a piece of work in 15 days and B alone in 20 days, in how many days can A alone complete the work ?
-
View Hint View Answer Discuss in Forum
(A + B)’s 1 day’s work = 1 15 B’s 1 day’s work = 1 20 ∴ A’s 1 day’s work = 1 - 1 15 20 A’s 1 day’s work = 4 - 3 = 1 60 60
∴ A alone will do the work in 60 days.
Second method to solve this question ,
Here , x = 15 , y = 20A alone do in = xy x - y
Correct Option: A
(A + B)’s 1 day’s work = 1 15 B’s 1 day’s work = 1 20 ∴ A’s 1 day’s work = 1 - 1 15 20 A’s 1 day’s work = 4 - 3 = 1 60 60
∴ A alone will do the work in 60 days.
Second method to solve this question ,
Here , x = 15 , y = 20A alone do in = xy x - y A alone do in = 15 × 20 20 - 15 A alone do in = 15 × 20 = 60 days. 5
- If A and B together can complete a work in 12 days, B and C together in 15 days and C and A together in 20 days, then B alone can complete the work in
-
View Hint View Answer Discuss in Forum
(A + B)’s 1 day’s work = 1 12
(B + C)’s 1 day’s work = 1 15 (C + A)’s 1 day’s work = 1 20
On adding ,2 (A + B + C)’s 1 day's work = 1 + 1 + 1 12 15 20 2 (A + B + C)’s 1 day's work = 5 + 4 + 3 = 1 60 5 ∴ (A+B+C)’s 1 day’s work = 1 10 ∴ B’s 1 day’s work = 1 - 1 10 20 B’s 1 day’s work = 2 -1 = 1 20 20
∴ B alone can do the work in 20 days.
Second method to solve this question ,
Here , x = 12 , y = 15 , z = 20
Correct Option: D
(A + B)’s 1 day’s work = 1 12
(B + C)’s 1 day’s work = 1 15 (C + A)’s 1 day’s work = 1 20
On adding ,2 (A + B + C)’s 1 day's work = 1 + 1 + 1 12 15 20 2 (A + B + C)’s 1 day's work = 5 + 4 + 3 = 1 60 5 ∴ (A+B+C)’s 1 day’s work = 1 10 ∴ B’s 1 day’s work = 1 - 1 10 20 B’s 1 day’s work = 2 -1 = 1 20 20
∴ B alone can do the work in 20 days.
Second method to solve this question ,
Here , x = 12 , y = 15 , z = 20Time taken = 2xyz -xy + yz + zx B alone can do in = 2 × 12 × 15 × 20 - 12 × 15 + 15 × 20 + 20 × 12 B alone can do in = 24 × 300 - 180 + 300 + 240 B alone can do in = 24 × 300 = 20 days. 360
