A boat travels 72 km downstream in 4 hours and 48 km upstream in 4 hours. Find the speed of the boat in still water.
Correct answer: 15 km/h
Explanation: Downstream=18, upstream=12. Still water speed=(18+12)/2=15 km/h.
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The ratio of the corresponding sides of two similar triangles is 5:8. Find the ratio of their areas.
Correct answer: 25:64
Explanation: Area ratio equals square of side ratio.
If x²−17x+60=0, find the sum of the reciprocals of the roots.
Correct answer: 17/60
Explanation: If roots are α,β then 1/α+1/β=(α+β)/αβ=17/60.
A train 240 m long crosses a platform in 30 seconds and a pole in 12 seconds. Find the length of the platform.
Correct answer: 360 m
Explanation: Speed=240/12=20 m/s. Distance in 30 s=600 m. Platform=600−240=360 m.
The average of 30 numbers is 52. If the average of the first 10 numbers is 48 and the average of the next 12 numbers is 55, find the average of the remaining 8 numbers.
Correct answer: 52.5
Explanation: Remaining total=1560−480−660=420. Average=420/8=52.5.
A can complete a work in 24 days, B in 40 days and C in 60 days. If all start together and A leaves after 8 days, approximately how many more days are required to finish the remaining work?
Correct answer: 6.4
Explanation: Remaining work=4/15. B+C rate=1/24. Time=(4/15)×24=6.4 days.
A trader marks an article 80% above cost price and allows a discount of 25%. Find the profit percentage.
Correct answer: 35%
Explanation: Assume CP=100. MP=180. SP=180×0.75=135. Profit =35%.
The HCF and LCM of two numbers are 28 and 1680 respectively. If one number is 336, find the other number.
Correct answer: 140
Explanation: Using Product = HCF × LCM, the other number = (28×1680)/336 = 140.
The least number which when divided by 15, 20 and 28 leaves remainder 4 in each case is
Correct answer: 424
Explanation: LCM(15,20,28)=420. Required number=420+4=424.
Find the simple interest on ₹24000 at 12% per annum for 2 years.
Correct answer: ₹5760
Explanation: SI=P×R×T/100 = 24000×12×2/100 = ₹5760.
A boat covers 60 km downstream in 4 hours and 36 km upstream in 4 hours. Find the speed of the stream.
Correct answer: 3 km/h
Explanation: Downstream=15, upstream=9. Stream=(15−9)/2=3 km/h.
The ratio of the radii of two spheres is 2:3. Find the ratio of their volumes.
Correct answer: 8:27
Explanation: Volume is proportional to cube of radius.
If x²−14x+45=0, find the difference between the roots.
Correct answer: 4
Explanation: Roots are 5 and 9. Difference = 4.
A train travelling at 72 km/h crosses another train of equal length moving in the opposite direction at 54 km/h in 10 seconds. Find the length of each train.
Correct answer: 175 m
Explanation: Relative speed=126 km/h=35 m/s. Combined length=350 m. Equal lengths=175 m each.
The average of 18 numbers is 42. If two numbers 36 and 48 are replaced by 54 and 60 respectively, find the new average.
Correct answer: 43.67
Explanation: Total increases by30. New average =42 + 30/18 = 43.67.
Two pipes can fill a tank in 12 hours and 18 hours respectively. An outlet can empty it in 36 hours. Find the time required when all three are opened together.
Correct answer: 8 hours
Explanation: Net rate = 1/12+1/18−1/36 = 1/8. Time = 8 hours.
A shopkeeper gives successive discounts of 15% and 20% on the marked price. What is the single equivalent discount?
Correct answer: 32%
Explanation: Equivalent discount = 15+20−(15×20/100)=32%.
If the HCF and LCM of two numbers are 21 and 1260 respectively, and one number is 315, find the other number.
Correct answer: 84
Explanation: Other number = (21×1260)/315 = 84.
The smallest perfect square divisible by 12, 18 and 30 is
Correct answer: 900
Explanation: LCM(12,18,30)=180=2²×3²×5. Multiply by5 to obtain 900.
A boat covers 48 km downstream in 4 hours and returns upstream in 6 hours. Find the speed of the boat in still water.
Correct answer: 10 km/h
Explanation: Downstream=12 km/h, upstream=8 km/h. Still-water speed=(12+8)/2=10 km/h.