1. A can do a work in 20 days. B can do the same work in 30 days. If both work together, how much will A get if total wages are ₹6000?Solution:Work ratio A:B = 1/20 : 1/30 = 3:2Total parts = 5A’s share = (3/5) × 6000 = ₹3600—
2. A and B together can do a work in 12 days. A alone can do it in 18 days. In how many days B alone can complete the work?Solution:A’s 1 day work = 1/18(A + B)’s 1 day work = 1/12B’s 1 day work = 1/12 – 1/18 = (3 – 2)/36 = 1/36So, B alone can do in 36 days.
3. A, B, C together do a job for ₹7200. A does 2/5 of the work, B does 1/3. Find C’s share.Solution:A’s share = (2/5) × 7200 = ₹2880B’s share = (1/3) × 7200 = ₹2400C’s share = 7200 – (2880 + 2400) = ₹1920Answer: ₹1920—
4. A and B can complete a work in 10 days and 15 days respectively. They work together for 5 days. What part of work is left?Solution:1 day work = A + B = 1/10 + 1/15 = (3+2)/30 = 1/65 days work = 5/6Work left = 1 – 5/6 = 1/6—
5. A can do a work in 24 days. He works for 6 days and leaves. B finishes remaining in 12 days. How long does B take to complete the whole work alone?Solution:A’s 6 days work = 6/24 = 1/4Remaining work = 3/4B does 3/4 work in 12 days → full work in = 12 × 4/3 = 16 days—
6. A, B, and C together can do a work in 8 days. A can do it in 16 days, B in 24 days. In how many days can C alone do it?Solution:A’s 1 day work = 1/16, B’s = 1/24(A + B + C)’s 1 day work = 1/8So, C’s 1 day work = 1/8 – (1/16 + 1/24)= 1/8 – (5/48) = (6 – 5)/48 = 1/48C can do it in 48 days—
7. A is twice as efficient as B. Together they do a job in 12 days. How long will B alone take?Solution:Let B = x work/day → A = 2xTogether = x + 2x = 3xWork = 12 × 3x = 36xB alone → 36x / x = 36 days—
8. A, B, and C are paid ₹12000 for a work. They work in ratio 3:2:1. What is B’s share?Solution:Total ratio = 3 + 2 + 1 = 6B’s share = (2/6) × 12000 = ₹4000—
9. A and B can do a work in 18 days. B and C in 24 days. A and C in 36 days. In how many days can A alone do the work?Solution:Let total work = LCM(18,24,36) = 72A+B = 72/18 = 4B+C = 72/24 = 3A+C = 72/36 = 2Adding all: 2(A+B+C) = 4+3+2 = 9 → A+B+C = 4.5A = A+B+C – (B+C) = 4.5 – 3 = 1.5So A’s 1 day work = 1.5 → A alone takes 72 / 1.5 = 48 days—
10. A does 60% of a work in 9 days. How many more days will he take to complete the rest?Solution:60% → 9 days → 1% = 9/60 = 0.15 daysRemaining 40% = 0.15 × 40 = 6 days.