1️⃣ A can do a piece of work in 10 days, and B can do the same work in 15 days. If they work together, how much of the work will they complete in 1 day?
2️⃣ A and B together can complete a work in 8 days. A alone can complete it in 12 days. How many days will B alone take to complete the work?
Step-by-Step Explanation
(A+B)'s 1-day work: 1/8
A's 1-day work: 1/12
B's 1-day work: 1/8 - 1/12 = (3-2)/24 = 1/24
B alone takes 24 days.
Answer: 24 days ✅
3️⃣ A can do a work in 20 days, and B can do the same work in 30 days. If they work together and receive ₹600, what is A's share?
Step-by-Step Explanation
A's 1-day work: 1/20
B's 1-day work: 1/30
Ratio of work done: 1/20 : 1/30 = 3:2
A's share: (3/5) * 600 = ₹360
Answer: ₹360 ✅
4️⃣ 3 men or 5 women can do a piece of work in 12 days. How many days will 6 men and 5 women take to do the same work?
Step-by-Step Explanation
3 men = 5 women, so 6 men = 10 women
6 men + 5 women = 10 women + 5 women = 15 women
5 women take 12 days, so 15 women take 12/3 = 4 days
Answer: 4 days ✅
5️⃣ A and B can do a piece of work in 10 days, B and C in 12 days, and C and A in 15 days. In how many days can A, B, and C together complete the work?
6️⃣ A can complete a task in 15 days, and B can complete it in 20 days. If they work together for 4 days, what fraction of the work is left?
Step-by-Step Explanation
A's 1-day work: 1/15
B's 1-day work: 1/20
(A+B)'s 1-day work: 1/15 + 1/20 = (4+3)/60 = 7/60
Work done in 4 days: 4 * (7/60) = 28/60 = 7/15
Work left: 1 - 7/15 = 8/15
Answer: 8/15 ✅
7️⃣ A and B undertake to do a piece of work for ₹450. A can do it in 20 days, and B can do it in 40 days. With the help of C, they finish it in 8 days. What is C's share?
8️⃣ A and B can complete a piece of work in 15 days. B and C can complete the same work in 20 days. If A's one day work is twice that of C's one day work, find the time taken by B alone to complete the work.
Step-by-Step Explanation
(A + B)'s 1-day work: 1/15
(B + C)'s 1-day work: 1/20
Let C's 1-day work be 'x'. Then A's 1-day work is '2x'.
From (B + C)'s work: B's 1-day work = 1/20 - x.
From (A + B)'s work: 2x + (1/20 - x) = 1/15
Simplify: x + 1/20 = 1/15
Solve for x: x = 1/15 - 1/20 = (4 - 3) / 60 = 1/60 (This is C's 1-day work)
9️⃣ A can do a piece of work in 18 days and B in 24 days. They worked together for 8 days and then A left. The remaining work was finished by B in how many days?
Step-by-Step Explanation
A's 1-day work: 1/18
B's 1-day work: 1/24
(A+B)'s 1-day work: 1/18 + 1/24 = (4+3)/72 = 7/72
Work done in 8 days: 8 * (7/72) = 56/72 = 7/9
Work left: 1 - 7/9 = 2/9
B finishes 2/9 work in (2/9)/(1/24) = 16/3 days.
Correct Answer: 16/3 days (Not in the options)
🔟 A can do a piece of work in 12 days, B can do it in 15 days, and C can do it in 20 days. If they all work together, how long will it take to complete the work?