Government exams
- 4 men or 6 women can finish a work in 12 days. How many days will 3 men and 3 women take to finish it? Answer: C. 9.6 days Answer: (C) 9.6 days 4 men = 6 women, so 1 woman = 2/3 man. 3 men + 3 women = 3 + 2 = 5 men. 4 men take 12 days, so 5 me... 1
- 12 men working 8 hours a day finish a job in 10 days. In how many days will 15 men working 6 hours a day finish it? Answer: A. 102/3 days Answer: (A) 102/3 days Shortcut: M₁D₁H₁ = M₂D₂H₂. 12 × 10 × 8 = 15 × D × 6, so D = 960/90 = 102/3 days. 1
- A can do a work in 20 days and B in 30 days. They start together, but A leaves after 5 days. In how many days in all is the work finished? Answer: A. 22.5 days Answer: (A) 22.5 days Work = 60 units; A = 3, B = 2 units/day. In 5 days together they do 25 units; 35 units remain. B... 1
- A can do a work in 6 days and B in 8 days. Working together they finish it and are paid ₹1,400. What is A's share? Answer: C. ₹800 Answer: (C) ₹800 Wages are shared in the ratio of work done, i.e. efficiencies. A : B = 1/6 : 1/8 = 4 : 3. A's share = 4/7 ×... 1
- A and B can do a work in 6 days. With the help of C they finish it in 4 days. How many days will C alone take? Answer: C. 12 days Answer: (C) 12 days Shortcut: C = 6 × 4/6 - 4 = 12 days. 1
- A can do a work in 10 days and B in 15 days. They work on alternate days, with A starting on the first day. In how many days will the work be finished? Answer: B. 12 days Answer: (B) 12 days Work = 30 units; A = 3 units/day, B = 2 units/day. Every 2 days, 5 units are done. 30 units need 6 su... 1
- 10 men can finish a job in 15 days. After they have worked for 5 days, 5 more men join them. In how many more days will the job be finished? Answer: D. 62/3 days Answer: (D) 62/3 days Remaining work = 10 men × 10 days = 100 man-days. Now 15 men work, so days = 100 ÷ 15 = 62/3 . 1
- A is four times as efficient as B and takes 45 days less than B to finish a work. How many days will they take working together? Answer: C. 12 days Answer: (C) 12 days If A takes x days, B takes 4x days. 4x − x = 45, so x = 15. B takes 60 days. Together = 15 × 60/75 =... 1
- A can do a work in 16 days and B in 12 days. With C's help they finish it in 4 days and are paid ₹3,600 in all. What is C's share? Answer: A. ₹1500 Answer: (A) ₹1500 In 4 days A does 4/16 = 1/4 of the work and B does 4/12 = 1/3 . C does 1 - 1/4 - 1/3 = 5/12 . C's share =... 1
- A can do a work in 15 days. He works for 5 days and then B finishes the rest in 9 days. How many days would B alone take to do the whole work? Answer: C. 13.5 days Answer: (C) 13.5 days A does 5/15 = 1/3 . B does the remaining 2/3 in 9 days, so B alone needs 9 × 3/2 = 13.5 days. 1
- A and B can do a work in 18 days, B and C in 24 days, and A and C in 36 days. How many days will A alone take? Answer: B. 48 days Answer: (B) 48 days Work = 72 units. A+B = 4, B+C = 3, A+C = 2 units/day. So A+B+C = 9 ÷ 2 = 4.5 units/day. A = 4.5 − (B+... 1
- 3 men and 4 boys can do a work in 11 days, while 4 men and 3 boys can do it in 10 days. How many days will 2 men and 1 boy take? Answer: B. 22 days Answer: (B) 22 days Let a man do m and a boy b of the work per day. 3m + 4b = 1/11 and 4m + 3b = 1/10 . Adding: 7(m + b)... 1
- A is twice as efficient as B. B starts a work alone and works for 5 days; then A joins him and together they finish the work in 5 more days. How many days would A alone take for the whole work? Answer: D. 10 days Answer: (D) 10 days Let B do 1 unit/day; then A does 2 units/day. Work = B's 5 days + (A+B) for 5 days = 5 × 1 + 5 × 3 =... 1
- A can do a work in 25 days and B in 20 days. They start together, but A leaves 5 days before the work is finished. In how many days is the work finished? Answer: B. 131/3 days Answer: (B) 131/3 days Let the total time be T days. A works (T − 5) days and B works T days. T - 5/25 + T/20 = 1 → 4(... 1
- A can do a work in 12 days and B in 15 days. They work together for 4 days and then both leave. C finishes the remaining work in 6 days. How many days would C alone take for the whole work? Answer: D. 15 days Answer: (D) 15 days Work = 60 units; A = 5, B = 4 units/day. In 4 days they do 36 units; 24 units are left. C does 24 uni... 1
- What amount will ₹8,000 become in 2 years at 5% per annum compound interest? Answer: A. ₹8820 Answer: (A) ₹8820 5% for 2 years = 10.25% effective. Amount = 8000 × 1.1025 = ₹8820. 1
- What is the difference between the compound interest and the simple interest on ₹5,000 for 2 years at 4% per annum? Answer: D. ₹8 Answer: (D) ₹8 Shortcut: for 2 years, CI − SI = P(R/100)² = 5000 × 16/10000 = ₹8. 1
- The simple interest on ₹4,500 for 4 years is ₹1,440. What is the rate of interest per annum? Answer: A. 8% Answer: (A) 8% R = SI × 100/P × T = 1440 × 100/4500 × 4 = 8% . 1
- At simple interest, a sum becomes three times itself in 10 years. What is the rate of interest per annum? Answer: B. 20% Answer: (B) 20% Three times means the interest is 2 × P, i.e. 200% in 10 years. Rate = 200 ÷ 10 = 20%. Trap: 30% uses 300% in... 1
- A sum at simple interest amounts to ₹9,800 in 5 years and to ₹12,005 in 8 years. What is the rate of interest per annum? Answer: D. 12% Answer: (D) 12% Interest for 3 years = 12,005 − 9,800 = ₹2205, so 1 year's interest = ₹735. Principal = 9,800 − 5 × 735 = ₹61... 1
- What is the compound interest on ₹16,000 for 1 year at 10% per annum, compounded half-yearly? Answer: B. ₹1640 Answer: (B) ₹1640 Half-yearly: rate = 5% per half-year, 2 periods. Effective = 5 + 5 + 0.25 = 10.25%. CI = 10.25% of 16,000... 1
- A sum of money doubles itself in 6 years at compound interest. In how many years will it become 8 times itself? Answer: A. 18 years Answer: (A) 18 years 8 = 2³, so it needs three doubling periods: 3 × 6 = 18 years. Trap: 42 years is what you get by tre... 1
- The difference between the compound interest and the simple interest on a sum for 3 years at 10% per annum is ₹93. What is the sum? Answer: C. ₹3000 Answer: (C) ₹3000 Shortcut: for 3 years, CI − SI = P(R/100)²(3 + R/100) = P × 0.01 × 3.1 = 0.031P . 0.031P = 93, so P = ₹30... 1
- The compound interest on a sum for 2 years at 5% per annum is ₹328. What is the sum? Answer: C. ₹3200 Answer: (C) ₹3200 5% for 2 years = 10.25% effective. 10.25% of P = 328, so P = 328 ÷ 0.1025 = ₹3200. 1