1.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?
यदि A और B मिलकर किसी कार्य को 15 दिनों में तथा B अकेले 20 दिनों में पूरा कर सकते हैं, तो A अकेले उस कार्य को कितने दिनों में पूरा कर सकता है?
A.60
B.45
C.40
D.30
Answer: Option A
Solution:1st method:
A and B complete a work in = 15 days
One day’s work of (A + B) = 1/15
B complete the work in = 20 days;
One day’s work of B = 1/20
Then, A’s one day’s work =1/15−1/20
=4−3/6
=1/60
Thus, A can complete the work in = 60 days.
2nd method:
(A + B)’s one day’s % work =100/15
= 6.66%
B’s one day’s % work =100/20
= 5%
A’s one day’s % work = 6.66 – 5 = 1.66%
Thus, A need =100/1.66
= 60 days to complete the work.
2. 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:
यदि A और B मिलकर एक काम को 18 दिनों में पूरा कर सकते हैं, A और C एक साथ 12 दिनों में, और B और C एक साथ 9 दिनों में पूरा कर सकते हैं, तो B अकेले उस काम को कितने दिनों में पूरा कर सकता है:
A. 18 days
B. 24 days
C. 30 days
D. 40 days
Answer: Option B
Solution: One day’s work of (A+B) =1/18……(1)
One day’s work of (A+C) =1/12…….(2)
One day’s work of (B+C)=1/9…….(3)
Adding (1), (2) and(3)
2× (A+B+C) =1/18+1/12+1/9
2(A+B+C) =1/4
One day’s work of
A+B+C=1/8
B=1/8− (A+C)
B=1/8−1/12
One day’s work of B=3−2/24
=1/24
Bneed24days
3. A and B together can complete a work in 3 days. They start together but after 2 days, B left the work. If the work is completed after two more days, B alone could do the work in
A और B मिलकर एक कार्य को 3 दिनों में पूरा कर सकते हैं। वे एक साथ शुरू करते हैं लेकिन 2 दिनों के बाद, B ने काम छोड़ दिया। यदि कार्य दो दिन बाद पूरा हो जाता है, तो बालोने कार्य कर सकता है
A. 5 days
B. 6 days
C. 9 days
D. 10 days
Answer: Option B
Solution:1st Method:
(A+B)’s one day’s work =1/3 part
(A+B) works 2 days together =2/3part
Remaining work =1−2/3
=1/3 part
1/3 part of work is completed by A in two days
Hence, one day’s work of A =1/6
Then, one day’s work of B =1/3−1/6
=1/6
So, B alone can complete the whole work in 6 days.
2nd Method:
(A+B)’s one day’s % work =100/3
= 33.3%
Work completed in 2 days = 66.6%
Remaining work = 33.4%
One day’s % work of A =33.4/2
= 16.7%
One day’s work of B = 33.4 – 16.7 = 16.7%
B alone can complete the work in,
=100/16.7
= 5.98 days
≈ 6 days.