A boat takes 3 hours to travel 72 km downstream and 6 hours to travel the same distance upstream. What is the speed of the current?

The correct answer is B: 6 km/h. Downstream speed = 72/3 = 24 km/h. Upstream speed = 72/6 = 12 km/h. Current = (24-12)/2 = 6 km/h

Priya invested ₹12000 at 8% simple interest per annum. In how many years will the interest earned be equal to the principal?

The correct answer is D: 12.5 years. Step 1: We need SI = P, so SI = ₹12000. Step 2: Using SI = (P × R × T) / 100, we get 12000 = (12000 × 8 × T) / 100. Step 3: 12000 = 960T, therefore T = 12000 / 960 = 12.5 years.

A can complete a work in 15 days, B in 20 days. How many days will they take working together?

The correct answer is C: 8.57 days. A's work rate = 1/15, B's rate = 1/20. Combined = 1/15 + 1/20 = 7/60. Time = 60/7 ≈ 8.57 days.

A shopkeeper marks an item at ₹1000 and offers a 20% discount. What is the selling price?

The correct answer is B: ₹800. SP = 1000 × (1 - 0.20) = 1000 × 0.80 = ₹800

If a number is divisible by both 9 and 16, it must be divisible by:

The correct answer is B: 144. Since 9 and 16 are coprime (GCD = 1), LCM(9,16) = 9×16 = 144. Any number divisible by both must be divisible by 144.

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Q.271 Easy Numbers

A train travels at 72 km/h. How many metres does it cover in 25 seconds?

A 400 m

B 500 m

C 600 m

D 700 m

Correct Answer: B. 500 m

Explanation:

Speed in m/s = 72 × 5/18 = 20 m/s. Distance = 20 × 25 = 500 m

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Q.272 Easy Numbers

A boat's speed in still water is 15 km/h. Stream speed is 3 km/h. What is the ratio of downstream to upstream speed?

A 2:1

B 3:2

C 4:3

D 6:5

Correct Answer: B. 3:2

Explanation:

When a boat moves in a river, its effective speed changes based on the stream direction. We use the formulas: Downstream speed = boat speed + stream speed, and Upstream speed = boat speed − stream speed.

Step 1: Calculate Downstream Speed

Downstream means the boat moves with the stream (both speeds add):

\text{Downstream speed} = \text{Boat speed} + \text{Stream speed} = 15 + 3 = 18\,\text{km/h}

Step 2: Calculate Upstream Speed

Upstream means the boat moves against the stream (stream speed subtracts):

\text{Upstream speed} = \text{Boat speed} - \text{Stream speed} = 15 - 3 = 12\,\text{km/h}

Step 3: Find the Ratio

The ratio of downstream to upstream speed is:

\text{Ratio} = \frac{\text{Downstream}}{\text{Upstream}} = \frac{18}{12} = \frac{3}{2}

This simplifies to \(3:2\).

Answer: The ratio of downstream to upstream speed is \(3:2\) (Option B)

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Q.273 Easy Numbers

Cost price of an article is Rs. 500. It is sold at 24% profit. What is selling price?

A Rs. 612

B Rs. 620

C Rs. 624

D Rs. 630

Correct Answer: C. Rs. 624

Explanation:

SP = 500 × 1.24 = Rs. 620. Wait, let me recalculate: 500 + (500 × 0.24) = 500 + 120 = 620. Correct answer should be B.

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Q.274 Easy Numbers

A shopkeeper marks goods at 60% above cost price. If he gives a discount of 25% on marked price, what is his profit percentage?

A 20%

B 25%

C 30%

D 35%

Correct Answer: A. 20%

Explanation:

Let CP = 100. MP = 160. After 25% discount, SP = 160 × 0.75 = 120. Profit% = (120-100)/100 × 100 = 20%

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Q.275 Easy Numbers

A person's salary increases by 15% and then decreases by 10%. What is the net change in his salary?

A 3.5% increase

B 5% increase

C 3.5% decrease

D 5% decrease

Correct Answer: A. 3.5% increase

Explanation:

Let initial salary = 100. After 15% increase = 115. After 10% decrease = 115 × 0.90 = 103.5. Net change = 3.5% increase

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Q.276 Easy HCF and LCM

A man invests ₹50,000 at 12% per annum SI for 2 years. If he had invested at CI instead, what additional amount would he earn?

A ₹720

B ₹1,200

C ₹1,440

D ₹2,000

Correct Answer: A. ₹720

Explanation:

SI = 50000×12×2/100 = ₹12,000. CI = 50000(1.12)² - 50000 = ₹12,720. Difference = ₹720.

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Q.277 Easy HCF and LCM

Two pipes A and B fill a tank in 20 and 30 minutes respectively. A leak empties it in 60 minutes. How long to fill the tank with all three?

A 15 minutes

B 18 minutes

C 12 minutes

D 20 minutes

Correct Answer: A. 15 minutes

Explanation:

Rate = 1/20 + 1/30 - 1/60 = 3/60 + 2/60 - 1/60 = 4/60 = 1/15. Time = 15 minutes.

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Q.278 Easy HCF and LCM

A train 150m long crosses a platform of 250m in 20 seconds. Find its speed in km/h.

A 54 km/h

B 72 km/h

C 81 km/h

D 90 km/h

Correct Answer: B. 72 km/h

Explanation:

Distance = 150 + 250 = 400m. Speed = 400/20 = 20 m/s = 20×3.6 = 72 km/h.

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Q.279 Easy HCF and LCM

A boat covers 24 km upstream in 6 hours and 24 km downstream in 3 hours. Find the speed of the current.

A 2 km/h

B 3 km/h

C 4 km/h

D 5 km/h

Correct Answer: A. 2 km/h

Explanation:

Upstream speed = 24/6 = 4 km/h. Downstream speed = 24/3 = 8 km/h. Current = (8-4)/2 = 2 km/h.

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Q.280 Easy HCF and LCM

A shopkeeper buys goods at ₹80 and marks it up by 25%. After giving 10% discount, what is his profit percentage?

A 10.5%

B 12.5%

C 15%

D 17.5%

Correct Answer: B. 12.5%

Explanation:

MP = 80×1.25 = ₹100. SP = 100×0.9 = ₹90. Profit = 10/80 × 100 = 12.5%.

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