Profit & Loss
Q501–Q517 | Cost Price · Selling Price · Discount · Marked Price
Q501EasyCGL+CHSL
A shopkeeper buys an article for ₹500 and sells it for ₹600. What is the profit percentage?
A15%
B20%
C25%
D10%
Show Answer
✔ B — 20%
Profit = 600 − 500 = ₹100. Profit% = (100/500) × 100 = 20%. ❌ A,C,D: wrong calculation.
Q502ModerateCGL+CHSL
An article is marked at ₹800 and sold at a discount of 15%. What is the selling price?
A₹640
B₹680
C₹700
D₹660
Show Answer
✔ B — ₹680
Discount = 15% of 800 = ₹120. SP = 800 − 120 = ₹680. ❌ A(₹640 = 20% discount), ❌ C,D: wrong.
Q503ModerateCGL+CHSL
A trader sells goods at a profit of 20%. If the cost price is ₹450, what is the selling price?
A₹520
B₹540
C₹560
D₹580
Show Answer
✔ B — ₹540
SP = CP × (1 + profit%/100) = 450 × 1.2 = ₹540. ❌ A,C,D: wrong.
Q504EasyCGL+CHSL
If SP = ₹350 and Loss% = 12.5%, find the CP.
A₹380
B₹390
C₹400
D₹410
Show Answer
✔ C — ₹400
CP = SP / (1 − Loss%/100) = 350 / 0.875 = ₹400. ❌ A,B,D: wrong.
Q505DifficultCGL only
A shopkeeper marks his goods 25% above cost price and allows a discount of 10%. Find his net profit %.
A10%
B12%
C12.5%
D15%
Show Answer
✔ C — 12.5%
Let CP = 100. MP = 125. SP = 125 × 0.9 = 112.5. Profit% = (12.5/100) × 100 = 12.5%. ❌ A,B,D: wrong.
Q506ModerateCGL+CHSL
A man sells two articles for ₹990 each. On one he gains 10% and on the other he loses 10%. What is the overall result?
ANo profit, no loss
B1% gain
C1% loss
D2% gain
Show Answer
✔ C — 1% loss
When two articles are sold at same SP with equal profit% and loss%, there is always a loss = (common %/10)² = (10/10)² = 1%. CP₁ = 900, CP₂ = 1100. Total CP = 2000, Total SP = 1980. Loss = ₹20, Loss% = 1%. ❌ A,B,D: wrong. Classic SSC trap question.
Q507ModerateCGL+CHSL
By selling 33 metres of cloth, a shopkeeper earns a profit equal to the SP of 11 metres. What is the profit %?
A25%
B33⅓%
C50%
D11%
Show Answer
✔ C — 50%
Profit = SP of 11 m. SP of 33m − CP of 33m = SP of 11m → CP of 33m = SP of 22m. Profit% = (11/22) × 100 = 50%. ❌ A,B,D: wrong.
Q508DifficultCGL only
A merchant sells an article for ₹1440 gaining 20%. What price should he have sold to gain 35%?
A₹1580
B₹1600
C₹1620
D₹1650
Show Answer
✔ C — ₹1620
CP = 1440/1.2 = ₹1200. Required SP = 1200 × 1.35 = ₹1620. ❌ A,B,D: wrong.
Q509EasyCGL+CHSL
A person sells a watch for ₹480 and loses 20%. Find the cost price.
A₹560
B₹575
C₹600
D₹620
Show Answer
✔ C — ₹600
CP = 480/(1 − 0.20) = 480/0.8 = ₹600. ❌ A,B,D: wrong.
Q510ModerateCGL+CHSL
A trader sells 5 oranges for ₹4 and buys 4 oranges for ₹3. What is the profit %?
A5%
B6%
C6⅔%
D5⅓%
Show Answer
✔ C — 6⅔%
SP per orange = 4/5 = 0.8. CP per orange = 3/4 = 0.75. Profit% = (0.05/0.75) × 100 = 6.67% = 6⅔%. ❌ A,B,D: wrong.
Q511DifficultCGL only
A dishonest shopkeeper sells at CP but uses a weight of 950 g instead of 1 kg. What is his gain %?
A5%
B5.26%
C4.76%
D5.5%
Show Answer
✔ B — 5.26%
Gain% = [(True weight − False weight) / False weight] × 100 = [(1000 − 950) / 950] × 100 = (50/950) × 100 ≈ 5.26%. ❌ A,C,D: wrong. SSC-favourite formula.
Q512ModerateCGL+CHSL
A shopkeeper purchases 12 articles for ₹10 and sells 10 articles for ₹12. Find the profit %.
A40%
B44%
C42%
D45%
Show Answer
✔ B — 44%
CP of 1 article = 10/12. SP of 1 article = 12/10. Profit% = [(12/10 − 10/12)/(10/12)] × 100 = [(144−100)/100] × 100/... Let CP = 10/12 per unit, SP = 12/10. Ratio SP/CP = (12/10)/(10/12) = (12×12)/(10×10) = 144/100. Profit = 44%. ❌ A,C,D: wrong.
Q513EasyCGL+CHSL
The cost price of 15 articles is equal to the selling price of 12 articles. What is the profit %?
A20%
B25%
C30%
D15%
Show Answer
✔ B — 25%
15 × CP = 12 × SP → SP/CP = 15/12 = 5/4. Profit% = (1/4) × 100 = 25%. ❌ A,C,D: wrong.
Q514ModerateCGL+CHSL
A trader gives a successive discount of 10% and 5%. The effective discount is:
A14.5%
B15%
C14%
D15.5%
Show Answer
✔ A — 14.5%
Effective discount = 10 + 5 − (10×5/100) = 15 − 0.5 = 14.5%. Formula: d₁ + d₂ − d₁d₂/100. ❌ B(simple addition, ignoring interaction), ❌ C,D: wrong.
Q515DifficultCGL only
A person bought two fans for ₹2400 each. He sold one at 10% profit and the other at 10% loss. If transport cost was ₹96, what is his overall profit or loss?
A₹96 loss
B₹144 loss
CNo profit no loss
D₹96 profit
Show Answer
✔ A — ₹96 loss
SP₁ = 2,400 × 1.1 = 2,640; SP₂ = 2,400 × 0.9 = 2,160 → total SP = ₹4,800.
Total cost = 4,800 + 96 (transport) = ₹4,896.
Loss = 4,896 − 4,800 = ₹96. (Equal % profit and loss on the same cost price cancel out.)
❌ B (₹144): wrong formula. ❌ C: ignores transport. ❌ D: wrong direction.
Total cost = 4,800 + 96 (transport) = ₹4,896.
Loss = 4,896 − 4,800 = ₹96. (Equal % profit and loss on the same cost price cancel out.)
❌ B (₹144): wrong formula. ❌ C: ignores transport. ❌ D: wrong direction.
Q516ModerateCGL+CHSL
An article's marked price is 40% more than its cost price. If a discount of 20% is given, what is the profit %?
A10%
B12%
C14%
D16%
Show Answer
✔ B — 12%
Let CP = 100. MP = 140. SP = 140 × 0.8 = 112. Profit% = 12%. ❌ A,C,D: wrong.
Q517AdvancedCGL only
A shopkeeper allows 20% discount on MP and still makes 20% profit. If CP is ₹480, what is the MP?
A₹680
B₹700
C₹720
D₹750
Show Answer
✔ C — ₹720
SP = 480 × 1.2 = ₹576. SP = MP × 0.8 → MP = 576/0.8 = ₹720. ❌ A,B,D: wrong.
Time & Work
Q518–Q534 | Individual Work · Combined Work · Pipes & Cisterns
Q518EasyCGL+CHSL
A can finish a job in 10 days and B can finish it in 15 days. In how many days can they finish it together?
A5
B6
C7
D8
Show Answer
✔ B — 6 days
Combined rate = 1/10 + 1/15 = 3/30 + 2/30 = 5/30 = 1/6. Time = 6 days. ❌ A,C,D: wrong.
Q519ModerateCGL+CHSL
A and B together can complete a work in 8 days. A alone takes 12 days. In how many days can B alone complete it?
A20
B24
C28
D30
Show Answer
✔ B — 24 days
B's rate = 1/8 − 1/12 = 3/24 − 2/24 = 1/24. B alone = 24 days. ❌ A,C,D: wrong.
Q520ModerateCGL+CHSL
A pipe can fill a tank in 6 hours and another pipe can empty it in 8 hours. If both are open together, how long to fill the tank?
A20 hours
B24 hours
C28 hours
D32 hours
Show Answer
✔ B — 24 hours
Net rate = 1/6 − 1/8 = 4/24 − 3/24 = 1/24. Time to fill = 24 hours. ❌ A,C,D: wrong.
Q521DifficultCGL only
A, B, C can complete a work in 10, 12, 15 days respectively. A and B work together for 4 days, then C alone completes it. How many days does C work?
A3
B4
C5
D6
Show Answer
✔ B — 4
Take total work = LCM(10, 12, 15) = 60 units. A = 6, B = 5, C = 4 units/day.
A + B in 4 days = 4 × 11 = 44 units. Remaining = 16 units → C needs 16 ÷ 4 = 4 days.
❌ A, C, D: wrong remaining work.
A + B in 4 days = 4 × 11 = 44 units. Remaining = 16 units → C needs 16 ÷ 4 = 4 days.
❌ A, C, D: wrong remaining work.
Q522EasyCGL+CHSL
If 8 workers can do a job in 12 days, how many workers are needed to complete it in 6 days?
A12
B14
C16
D18
Show Answer
✔ C — 16 workers
Workers × Days = constant. 8 × 12 = N × 6 → N = 96/6 = 16. ❌ A,B,D: wrong.
Q523ModerateCGL+CHSL
A man takes 8 hours to complete a job. A woman takes 10 hours. A boy takes 40 hours. All three work together; how long to finish?
A3 hrs 20 min
B3 hrs 45 min
C4 hrs
D4 hrs 10 min
Show Answer
✔ C — 4 hrs
Combined rate = 1/8 + 1/10 + 1/40 = 5/40 + 4/40 + 1/40 = 10/40 = 1/4 per hour → 4 hours.
❌ A, B, D: wrong combined rate.
❌ A, B, D: wrong combined rate.
Q524ModerateCGL+CHSL
P can complete a work in 18 days and Q can do it in 9 days. Q works for 3 days and leaves. In how many more days will P finish the remaining work?
A12
B13
C14
D15
Show Answer
✔ A — 12 days
Q's 3-day work = 3/9 = 1/3. Remaining = 2/3. P completes 2/3 in = (2/3) × 18 = 12 days. ❌ B,C,D: wrong.
Q525DifficultCGL only
Tap A fills a tank in 12 min, Tap B fills in 15 min, Tap C empties in 6 min. All three are opened. When will the tank be full?
ATank never fills
B60 min
C30 min
D120 min
Show Answer
✔ A — Tank never fills
Net rate = 1/12 + 1/15 − 1/6 = 5/60 + 4/60 − 10/60 = −1/60. Negative rate means tank empties, never fills. ❌ B,C,D: wrong.
Q526ModerateCGL+CHSL
A can do a work in 15 days and B in 20 days. They work together for 4 days and then A leaves. How many more days will B take to finish?
A8
B10
C11
D12
Show Answer
✔ C — 11 days
A+B combined rate = 1/15 + 1/20 = 4/60 + 3/60 = 7/60. Work in 4 days = 28/60 = 7/15. Remaining = 8/15. B's rate = 1/20. Time = (8/15)×20 = 160/15 = 32/3 ≈ 10.67 ≈ 11 days. ❌ A,B,D: wrong.
Q527EasyCGL+CHSL
If 6 workers can build a wall in 9 days working 8 hours daily, how many days will 12 workers take working 6 hours daily?
A5
B6
C7
D8
Show Answer
✔ B — 6 days
Total work = 6 × 9 × 8 = 432 man-hours. New: 432 = 12 × D × 6 = 72D → D = 6 days. ❌ A,C,D: wrong.
Q528DifficultCGL only
A cistern is normally filled in 8 hours but takes 2 hours longer due to a leak at the bottom. If the cistern is full, in how many hours will the leak empty it?
A32
B36
C40
D45
Show Answer
✔ C — 40 hours
Without leak: fills in 8h. With leak: fills in 10h. Inlet rate = 1/8. Effective rate = 1/10. Leak rate = 1/8 − 1/10 = (5−4)/40 = 1/40. Leak empties full cistern in 40 hours. ❌ A,B,D: wrong.
Q529ModerateCGL+CHSL
A woman can finish a work in 12 days. After 4 days, her daughter joins her. They complete the rest in 4 more days. In how many days can the daughter alone finish the work?
A12
B14
C16
D18
Show Answer
✔ A — 12 days
Woman's 4-day work = 4/12 = 1/3. Remaining = 2/3. In 4 more days, both finish 2/3. Combined rate = (2/3)/4 = 1/6. Daughter's rate = 1/6 − 1/12 = 2/12 − 1/12 = 1/12. Daughter alone = 12 days. ❌ B,C,D: wrong.
Q530ModerateCGL+CHSL
Two pipes A and B can fill a tank in 20 min and 30 min respectively. Both are opened simultaneously. After how many minutes should B be closed so the tank fills in exactly 16 minutes?
A6
B8
C10
D12
Show Answer
✔ A — 6
A works all 16 minutes: 16/20 = 4/5 of the tank.
B must fill the other 1/5: t/30 = 1/5 → t = 6 minutes.
❌ B (8), C (10), D (12): the tank would overflow before 16 minutes.
B must fill the other 1/5: t/30 = 1/5 → t = 6 minutes.
❌ B (8), C (10), D (12): the tank would overflow before 16 minutes.
Q531EasyCGL+CHSL
20 men complete a work in 30 days. How many men are needed to complete 1.5 times the work in 25 days?
A30
B36
C40
D45
Show Answer
✔ B — 36 men
Men × Days = Work. 20 × 30 = 600 units. New work = 1.5 × 600 = 900. N × 25 = 900. N = 36. ❌ A,C,D: wrong.
Q532ModerateCGL+CHSL
A and B can do a work in 30 and 40 days. They started together but A left after some days and B completed the rest in 25 days. After how many days did A leave?
A5
B6
C7
D8
Show Answer
✔ B — 6 days
B's 25-day work = 25/40 = 5/8. Remaining = 3/8 done by A+B together. A+B rate = 1/30 + 1/40 = 7/120. Days together = (3/8)÷(7/120) = (3/8)×(120/7) = 360/56 = 45/7 ≈ 6.4 ≈ 6 days. ❌ A,C,D: wrong.
Q533DifficultCGL only
A fills a tank in 10 min, B in 15 min. They are opened together. After 3 min a hole develops that can empty the full tank in 8 min. How long does it take to fill the tank after the hole opens?
A9 min
B10 min
C12 min
D15 min
Show Answer
✔ C — 12 min
A + B = 1/10 + 1/15 = 1/6 per min; in 3 min = 1/2 filled.
With the hole: 1/6 − 1/8 = 1/24 per min.
Remaining 1/2 ÷ 1/24 = 12 min.
❌ A, B, D: wrong net rate.
With the hole: 1/6 − 1/8 = 1/24 per min.
Remaining 1/2 ÷ 1/24 = 12 min.
❌ A, B, D: wrong net rate.
Q534ModerateCGL+CHSL
If 12 men or 18 women can reap a field in 14 days, in how many days can 8 men and 16 women reap it?
A7
B9
C10
D12
Show Answer
✔ B — 9 days
12 men = 18 women → 1 man = 3/2 women. 8 men = 12 women. 8 men + 16 women = 12 + 16 = 28 women. 18 women take 14 days → 28 women take (18×14)/28 = 252/28 = 9 days. ❌ A,C,D: wrong.
Time, Speed & Distance
Q535–Q550 | Average Speed · Relative Speed · Trains · Boats & Streams
Q535EasyCGL+CHSL
A car travels 120 km in 2 hours. What is its speed in m/s?
A15 m/s
B16.67 m/s
C18 m/s
D20 m/s
Show Answer
✔ B — 16.67 m/s
Speed = 120/2 = 60 km/h = 60 × (5/18) m/s = 300/18 = 50/3 ≈ 16.67 m/s. ❌ A,C,D: wrong.
Q536ModerateCGL+CHSL
A train 200 m long passes a pole in 10 seconds. What is the speed of the train in km/h?
A60
B68
C72
D80
Show Answer
✔ C — 72 km/h
Speed = 200/10 = 20 m/s = 20 × (18/5) = 72 km/h. ❌ A,B,D: wrong.
Q537ModerateCGL+CHSL
A train 300 m long crosses a platform 200 m long in 25 seconds. What is the train's speed?
A60 km/h
B72 km/h
C54 km/h
D80 km/h
Show Answer
✔ B — 72 km/h
Distance = 300 + 200 = 500 m. Speed = 500/25 = 20 m/s = 72 km/h. ❌ A,C,D: wrong.
Q538DifficultCGL only
Two trains 150 m and 200 m long run at 54 km/h and 36 km/h in opposite directions. How long do they take to pass each other?
A10 sec
B12 sec
C14 sec
D15 sec
Show Answer
✔ C — 14 sec
Opposite directions: relative speed = 54 + 36 = 90 km/h = 25 m/s.
Distance = 150 + 200 = 350 m → time = 350 ÷ 25 = 14 seconds.
❌ A, B, D: wrong speed conversion or distance.
Distance = 150 + 200 = 350 m → time = 350 ÷ 25 = 14 seconds.
❌ A, B, D: wrong speed conversion or distance.
Q539EasyCGL+CHSL
A boat goes 30 km upstream in 3 hours and 30 km downstream in 2 hours. What is the speed of the stream?
A2.5 km/h
B3 km/h
C3.5 km/h
D4 km/h
Show Answer
✔ A — 2.5 km/h
Upstream speed = 10 km/h. Downstream speed = 15 km/h. Stream speed = (15−10)/2 = 2.5 km/h. ❌ B,C,D: wrong.
Q540ModerateCGL+CHSL
A man can row 7 km/h in still water. If the river flows at 3 km/h, how long to row 14 km upstream and return?
A4 hrs
B4.5 hrs
C4.9 hrs
D5.5 hrs
Show Answer
✔ C — 4.9 hrs
Upstream = 7 − 3 = 4 km/h; downstream = 7 + 3 = 10 km/h.
Time = 14/4 + 14/10 = 3.5 + 1.4 = 4.9 hours.
❌ A, B, D: wrong speeds.
Time = 14/4 + 14/10 = 3.5 + 1.4 = 4.9 hours.
❌ A, B, D: wrong speeds.
Q541DifficultCGL only
A man covers a distance at 8 km/h and returns at 12 km/h. What is his average speed for the whole journey?
A9.6 km/h
B10 km/h
C9.5 km/h
D10.5 km/h
Show Answer
✔ A — 9.6 km/h
Average speed = 2uv/(u+v) = 2×8×12/(8+12) = 192/20 = 9.6 km/h. ❌ B(simple average, wrong), ❌ C,D: wrong.
Q542ModerateCGL+CHSL
Two people start from the same point in opposite directions at 5 km/h and 7 km/h. After how many hours are they 36 km apart?
A2
B3
C4
D5
Show Answer
✔ B — 3 hours
Relative speed = 5 + 7 = 12 km/h (opposite directions). Time = 36/12 = 3 hours. ❌ A,C,D: wrong.
Q543ModerateCGL+CHSL
A person travels from A to B at 60 km/h and B to A at 40 km/h. If total time is 5 hours, what is the distance AB?
A100 km
B110 km
C120 km
D125 km
Show Answer
✔ C — 120 km
Let d = AB. d/60 + d/40 = 5 → d(2+3)/120 = 5 → 5d/120 = 5 → d = 120 km. ❌ A,B,D: wrong.
Q544DifficultCGL only
A thief runs at 10 km/h. A policeman chases at 14 km/h. If the thief has a 50-metre head start, how long does the policeman take to catch the thief?
A45 seconds
B30 seconds
C40 seconds
D50 seconds
Show Answer
✔ A — 45 seconds
Relative speed = 14 − 10 = 4 km/h = 4,000/3,600 = 10/9 m/s.
Time to close 50 m = 50 ÷ (10/9) = 45 seconds.
❌ B (30 s), C (40 s), D (50 s): wrong speed conversion.
Time to close 50 m = 50 ÷ (10/9) = 45 seconds.
❌ B (30 s), C (40 s), D (50 s): wrong speed conversion.
Q545EasyCGL+CHSL
A train running at 54 km/h takes 20 seconds to cross a man standing on a platform. What is the length of the train?
A250 m
B280 m
C300 m
D320 m
Show Answer
✔ C — 300 m
Speed = 54 × 5/18 = 15 m/s. Length = 15 × 20 = 300 m. ❌ A,B,D: wrong.
Q546ModerateCGL+CHSL
Walking at 3/4 of his usual speed, a person is 24 minutes late. What is his usual time to reach the destination?
A60 min
B66 min
C72 min
D78 min
Show Answer
✔ C — 72 min
At 3/4 speed, time = 4/3 of usual. Extra time = (4/3 − 1) × usual = (1/3) × usual = 24 min. Usual time = 72 min. ❌ A,B,D: wrong.
Q547DifficultCGL only
Two trains start at the same time from stations P and Q, 630 km apart, heading towards each other at 60 and 90 km/h. Where will they meet from P?
A240 km
B252 km
C260 km
D270 km
Show Answer
✔ B — 252 km
Time to meet = 630/(60+90) = 630/150 = 4.2 hours. Distance from P = 60 × 4.2 = 252 km. ❌ A,C,D: wrong.
Q548ModerateCGL+CHSL
A man cycled 2/5 of his journey at 15 km/h and the rest at 10 km/h. If total distance = 50 km, find total time.
A3 h 20 min
B3 h 40 min
C4 h
D4 h 20 min
Show Answer
✔ D — 4 h 20 min
First 2/5 of 50 km = 20 km at 15 km/h → 4/3 h = 1 h 20 min.
Remaining 30 km at 10 km/h → 3 h.
Total = 4 h 20 min.
❌ A, B, C: wrong split of the distance.
Remaining 30 km at 10 km/h → 3 h.
Total = 4 h 20 min.
❌ A, B, C: wrong split of the distance.
Q549ModerateCGL+CHSL
A speed boat travels 60 km downstream in 2 hours. If the stream's speed is 5 km/h, how long to travel 60 km upstream?
A3 hrs
B4 hrs
C5 hrs
D6 hrs
Show Answer
✔ A — 3 hrs
Downstream speed = 60/2 = 30 km/h = boat + 5 → boat = 25 km/h.
Upstream = 25 − 5 = 20 km/h → 60/20 = 3 hours.
❌ B, C, D: wrong boat speed.
Upstream = 25 − 5 = 20 km/h → 60/20 = 3 hours.
❌ B, C, D: wrong boat speed.
Q550DifficultCGL only
A car covers a distance in 8 hours. If it increases speed by 15 km/h, it takes 6 hours. What is the original speed?
A40 km/h
B45 km/h
C50 km/h
D55 km/h
Show Answer
✔ B — 45 km/h
Distance = Speed × Time. 8s = 6(s+15) → 8s = 6s + 90 → 2s = 90 → s = 45 km/h. ❌ A,C,D: wrong.