Quantitative Aptitude (SSC)

Algebra Averages Boats & Streams Data Interpretation Geometry HCF & LCM Mensuration Mixtures & Alligation Number System Partnerships Percentages Profit, Loss & Discount Ratio & Proportion Simple & Compound Interest Simplification Time & Work Time, Speed & Distance Trigonometry

Q. A boat travels 15 km upstream in 3 hours. If the speed of the stream is 3 km/h, what is the speed of the boat in still water?

A. 6 km/h
B. 9 km/h
C. 12 km/h
D. 15 km/h

Solution

Speed upstream = 15 / 3 = 5 km/h. Speed of boat = Speed upstream + Speed of stream = 5 + 3 = 8 km/h.

Correct Answer: B — 9 km/h

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Q. A boat travels 20 km upstream and 30 km downstream in a total time of 5 hours. If the speed of the stream is 2 km/h, what is the speed of the boat in still water?

A. 8 km/h
B. 10 km/h
C. 12 km/h
D. 14 km/h

Solution

Let speed of boat = x km/h. Time upstream = 20 / (x - 2) and time downstream = 30 / (x + 2). Thus, (20 / (x - 2)) + (30 / (x + 2)) = 5. Solving gives x = 12 km/h.

Correct Answer: B — 10 km/h

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Q. A boat travels 30 km downstream and returns upstream in a total time of 5 hours. If the speed of the stream is 2 km/h, what is the speed of the boat in still water?

A. 8 km/h
B. 10 km/h
C. 12 km/h
D. 14 km/h

Solution

Let speed of boat = x km/h. Time downstream = 30/(x+2) and upstream = 30/(x-2). Total time = 30/(x+2) + 30/(x-2) = 5. Solving gives x = 10 km/h.

Correct Answer: B — 10 km/h

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Q. A boat travels 40 km downstream and 30 km upstream in a total time of 6 hours. If the speed of the stream is 4 km/h, what is the speed of the boat in still water?

A. 10 km/h
B. 12 km/h
C. 14 km/h
D. 16 km/h

Solution

Let speed of boat = x km/h. Time downstream = 40 / (x + 4) and time upstream = 30 / (x - 4). Thus, (40 / (x + 4)) + (30 / (x - 4)) = 6. Solving gives x = 14 km/h.

Correct Answer: B — 12 km/h

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Q. A boat travels 40 km downstream in 3 hours. If the speed of the current is 4 km/h, what is the speed of the boat in still water?

A. 10 km/h
B. 12 km/h
C. 14 km/h
D. 16 km/h

Solution

Speed downstream = 40 / 3 = 13.33 km/h. Speed in still water = Speed downstream - Speed of current = 13.33 - 4 = 9.33 km/h.

Correct Answer: C — 14 km/h

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Q. A boat travels 50 km upstream and 70 km downstream in a total time of 10 hours. If the speed of the boat in still water is 15 km/h, what is the speed of the current?

A. 2 km/h
B. 3 km/h
C. 4 km/h
D. 5 km/h

Solution

Let the speed of current be x km/h. Time upstream = 50/(15-x) and time downstream = 70/(15+x). Setting up the equation: 50/(15-x) + 70/(15+x) = 10.

Correct Answer: C — 4 km/h

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Q. A boat travels 60 km downstream in 3 hours. If the speed of the boat in still water is 20 km/h, what is the speed of the stream?

A. 5 km/h
B. 10 km/h
C. 15 km/h
D. 20 km/h

Solution

Speed downstream = Distance / Time = 60 / 3 = 20 km/h. Speed of stream = Speed downstream - Speed of boat = 20 - 20 = 0 km/h.

Correct Answer: B — 10 km/h

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Q. A boat travels 60 km downstream in 3 hours. If the speed of the boat in still water is 20 km/h, what is the speed of the current?

A. 5 km/h
B. 10 km/h
C. 15 km/h
D. 20 km/h

Solution

Speed downstream = Distance/Time = 60 km / 3 hours = 20 km/h. Speed of current = Speed downstream - Speed in still water = 20 km/h - 20 km/h = 0 km/h.

Correct Answer: B — 10 km/h

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Q. A boat travels 60 km downstream in 4 hours. If the speed of the stream is 5 km/h, what is the speed of the boat in still water?

A. 10 km/h
B. 15 km/h
C. 20 km/h
D. 25 km/h

Solution

Speed downstream = 60 km / 4 h = 15 km/h. Speed of boat = Speed downstream - Speed of stream = 15 - 5 = 10 km/h.

Correct Answer: C — 20 km/h

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Q. A boat travels 90 km downstream in 6 hours. If the speed of the current is 3 km/h, what is the speed of the boat in still water?

A. 12 km/h
B. 15 km/h
C. 18 km/h
D. 21 km/h

Solution

Speed downstream = 90 / 6 = 15 km/h. Speed in still water = Speed downstream - Speed of current = 15 - 3 = 12 km/h.

Correct Answer: B — 15 km/h

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Q. A boat travels downstream at a speed of 15 km/h and takes 2 hours to cover a distance. What is the distance covered?

A. 30 km
B. 25 km
C. 20 km
D. 15 km

Solution

Distance = Speed × Time = 15 km/h × 2 hours = 30 km.

Correct Answer: A — 30 km

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Q. A boat travels downstream for 4 hours at a speed of 15 km/h. How far has it traveled?

A. 45 km
B. 60 km
C. 75 km
D. 90 km

Solution

Distance = Speed × Time = 15 km/h × 4 h = 60 km.

Correct Answer: D — 90 km

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Q. A book is marked at $200. If it is sold for $160, what is the percentage discount given?

A. 20%
B. 25%
C. 30%
D. 35%

Solution

Discount = Marked Price - Selling Price = 200 - 160 = $40. Percentage Discount = (40/200) * 100 = 20%.

Correct Answer: B — 25%

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Q. A book is marked at $50. If it is sold for $40, what is the percentage discount given?

A. 20%
B. 25%
C. 30%
D. 15%

Solution

Discount = Marked Price - Selling Price = 50 - 40 = 10. Percentage Discount = (10/50) * 100 = 20%.

Correct Answer: B — 25%

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Q. A book is sold for $45 after a discount of 10%. What is the marked price?

A. $50
B. $55
C. $60
D. $65

Solution

Let the marked price be x. Selling Price = x - 0.10x = 0.90x. So, 0.90x = 45. Therefore, x = 45 / 0.90 = 50.

Correct Answer: A — $50

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Q. A book is sold for $45 after a discount of 10%. What was the marked price?

A. $50
B. $55
C. $60
D. $65

Solution

Let the marked price be x. Selling Price = x - 10% of x = x - 0.1x = 0.9x. Therefore, 0.9x = 45. x = 45 / 0.9 = 50.

Correct Answer: A — $50

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Q. A book is sold for $45 after a discount of 10%. What was the original price of the book?

A. $50
B. $55
C. $60
D. $65

Solution

Let the original price be x. Selling Price = x - 0.10x = 0.90x. Therefore, 0.90x = 45. x = 45 / 0.90 = $50.

Correct Answer: A — $50

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Q. A book is sold for $45 after a discount of 10%. What was the original price?

A. $50
B. $55
C. $60
D. $45

Solution

Let the original price be x. After a 10% discount, Selling Price = x - 0.1x = 0.9x. 0.9x = 45, x = 45/0.9 = 50.

Correct Answer: A — $50

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Q. A book's price is decreased by 10% and the new price is $18. What was the original price?

A. $20
B. $22
C. $19
D. $21

Solution

Let the original price be x. Then, x - 0.1x = 18 => 0.9x = 18 => x = 18 / 0.9 = $20.

Correct Answer: A — $20

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Q. A book's price is decreased by 20% and the new price is $24. What was the original price?

A. $30
B. $28
C. $26
D. $25

Solution

Let original price be x. Then, x - 0.2x = 24 => 0.8x = 24 => x = 24 / 0.8 = $30.

Correct Answer: A — $30

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Q. A book's price is increased by 10% and then decreased by 10%. If the original price was $100, what is the final price?

A. $100
B. $99
C. $90
D. $95

Solution

New Price after increase = 100 + (10% of 100) = 100 + 10 = $110. Final Price after decrease = 110 - (10% of 110) = 110 - 11 = $99.

Correct Answer: A — $100

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Q. A book's price is increased by 15% to $23. What was the original price of the book?

A. $20
B. $21
C. $22
D. $19

Solution

Original Price = New Price / (1 + 0.15) = 23 / 1.15 = $20.

Correct Answer: A — $20

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Q. A book's price is increased from $15 to $18. What is the percentage increase in the price?

A. 20%
B. 15%
C. 25%
D. 10%

Solution

Percentage Increase = ((New Price - Original Price) / Original Price) * 100 = ((18 - 15) / 15) * 100 = (3 / 15) * 100 = 20%.

Correct Answer: A — 20%

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Q. A box contains 3 red balls and 5 blue balls. What is the probability of picking a red ball?

A. 3/8
B. 5/8
C. 1/2
D. 1/3

Solution

Total balls = 3 + 5 = 8. Probability of red ball = 3/8.

Correct Answer: A — 3/8

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Q. A bus leaves a station and travels at a speed of 50 km/h. If it travels for 3 hours, how far will it have traveled?

A. 120 km
B. 130 km
C. 140 km
D. 150 km

Solution

Distance = Speed × Time = 50 km/h × 3 h = 150 km.

Correct Answer: D — 150 km

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Q. A bus travels at a speed of 50 km/h. If it takes 3 hours to reach its destination, how far is the destination?

A. 120 km
B. 130 km
C. 140 km
D. 150 km

Solution

Distance = Speed × Time = 50 km/h × 3 h = 150 km.

Correct Answer: D — 150 km

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Q. A bus travels at a speed of 50 km/h. If it takes 3 hours to reach its destination, what is the distance covered?

A. 120 km
B. 130 km
C. 150 km
D. 160 km

Solution

Distance = Speed × Time = 50 km/h × 3 h = 150 km.

Correct Answer: C — 150 km

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Q. A can complete a work in 10 days, while B can complete the same work in 15 days. If both work together, how many days will they take to complete the work?

A. 5
B. 6
C. 7
D. 8

Solution

A's work rate = 1/10, B's work rate = 1/15. Combined rate = 1/10 + 1/15 = 1/6. They will complete the work in 6 days.

Correct Answer: B — 6

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Q. A can complete a work in 8 days, B can complete it in 12 days. If they work together for 4 days, how much work is left?

A. 1/3
B. 1/4
C. 1/5
D. 1/6

Solution

A's rate = 1/8, B's rate = 1/12. Combined rate = 1/8 + 1/12 = 5/24. In 4 days, they complete 20/24 = 5/6 of the work. Remaining = 1/6.

Correct Answer: B — 1/4

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Q. A can complete a work in 8 days, B in 12 days, and C in 24 days. If they work together for 2 days, how much work is left?

A. 1/4
B. 1/3
C. 1/2
D. 1/6

Solution

A's rate = 1/8, B's rate = 1/12, C's rate = 1/24. Combined rate = 1/8 + 1/12 + 1/24 = 1/4. Work done in 2 days = 2/4 = 1/2. Remaining work = 1 - 1/2 = 1/2.

Correct Answer: B — 1/3

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Quantitative Aptitude (SSC)

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