A man invests ₹10,000 at 15% SI for 2 years. He then invests the entire amount (principal + SI) for next 3 years at 12% CI. Find total amount after 5 years.

The correct answer is A: ₹18,264.06. This problem involves two sequential investments: first at simple interest, then the accumulated amount at compound interest. **Step 1: Calculate Simple Interest for first 2 years** Using the Simple Interest formula $SI = \frac{P \times R \times T}{100}$: \[SI = \frac{10,000 \times 15 \times 2}{10

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?

The correct answer is A: 15 minutes. Rate = 1/20 + 1/30 - 1/60 = 3/60 + 2/60 - 1/60 = 4/60 = 1/15. Time = 15 minutes.

Two trains of lengths 200m and 150m travel towards each other at 60 km/h and 40 km/h respectively. Time to cross each other is?

The correct answer is B: 12.6 seconds. When two trains travel towards each other, their relative speed is the sum of their individual speeds, and they must cover a combined distance equal to the sum of their lengths. **Step 1: Convert Speeds to m/s** [Since speeds are given in km/h, we convert them to m/s by multiplying by 5/18] $$\text{

Three bells ring at intervals of 8, 12, and 18 minutes. If they ring together at 9:00 AM, when will they ring together again?

The correct answer is B: 10:12 AM. LCM(8,12,18) = 72 minutes. 9:00 AM + 72 minutes = 10:12 AM.

A man invests Rs. 10000 in two schemes at 12% and 15% per annum SI respectively. If total interest after 3 years is Rs. 4050, how much was invested in the first scheme?

The correct answer is C: Rs. 5000. Let amount in scheme 1 = x. Amount in scheme 2 = 10000-x. Interest = (x×12×3)/100 + ((10000-x)×15×3)/100 = 4050. 36x + 450000 - 45x = 405000. -9x = -45000. x = 5000

Central Govt Exam Preparation — SSC, UPSC, Bank, Railway

Q.351 Medium HCF and LCM

A train traveling at 60 km/h crosses a platform 300m long in 30 seconds. What is the length of the train?

A 200m

B 300m

C 400m

D 500m

Correct Answer: A. 200m

Explanation:

When a train crosses a platform, it must travel a distance equal to its own length plus the platform length. We'll use the relationship between speed, distance, and time.

Step 1: Convert speed to m/s

The train travels at $60\,\text{km/h}$. Convert to metres per second:

60\,\text{km/h} = 60 \times \frac{1000}{3600} = \frac{60000}{3600} = \frac{50}{3}\,\text{m/s}

Step 2: Calculate total distance traveled

The train crosses the platform in 30 seconds. Using $\text{Distance} = \text{Speed} \times \text{Time}$:

\text{Distance} = \frac{50}{3} \times 30 = \frac{1500}{3} = 500\,\text{m}

Step 3: Apply the crossing condition

When a train crosses a platform, the total distance it travels equals the train's length plus the platform's length:

\text{Train length} + \text{Platform length} = \text{Total distance}

\text{Train length} + 300 = 500

Step 4: Solve for train length

\text{Train length} = 500 - 300 = 200\,\text{m}

Answer: The length of the train is $200\,\text{m}$ (Option A)

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Q.352 Medium HCF and LCM

A boat travels 48 km downstream in 3 hours and 24 km upstream in 4 hours. Find the speed of the boat in still water.

A 10 km/h

B 12 km/h

C 14 km/h

D 16 km/h

Correct Answer: A. 10 km/h

Explanation:

Downstream speed = 48/3 = 16 km/h. Upstream speed = 24/4 = 6 km/h. Speed in still water = (16+6)/2 = 11 km/h. (Closest option A is 10, likely ₹typo in question setup)

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Q.353 Medium HCF and LCM

HCF of 96, 144, and 192 is?

A 24

B 32

C 48

D 64

Correct Answer: C. 48

Explanation:

96 = 2^5 × 3, 144 = 2^4 × 3^2, 192 = 2^6 × 3. HCF = 2^4 × 3 = 16 × 3 = 48

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Q.354 Medium HCF and LCM

Compound Interest on ₹8000 at 10% per annum for 2 years is?

A ₹1600

B ₹1680

C ₹1720

D ₹1800

Correct Answer: B. ₹1680

Explanation:

Amount = P(1 + r/100)^t = 8000(1.1)^2 = 8000 × 1.21 = ₹9680. CI = 9680 - 8000 = ₹1680

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Q.355 Medium HCF and LCM

A man sells two articles. One at 20% profit and another at 20% loss. If both have the same cost price of ₹1000, what is the overall profit or loss?

A No profit, no loss

B 4% profit

C 4% loss

D 5% profit

Correct Answer: A. No profit, no loss

Explanation:

When selling multiple articles at different profit/loss percentages with equal cost prices, we calculate the overall result by comparing total selling price to total cost price.

Step 1: Calculate selling price of first article (20% profit)

Cost price of first article = ₹1000

Selling price with 20% profit:

S_1 = 1000 + 20\% \text{ of } 1000 = 1000 + 0.20 \times 1000 = ₹1200

Step 2: Calculate selling price of second article (20% loss)

Cost price of second article = ₹1000

Selling price with 20% loss:

S_2 = 1000 - 20\% \text{ of } 1000 = 1000 - 0.20 \times 1000 = ₹800

Step 3: Find total cost price and total selling price

\text{Total Cost Price} = 1000 + 1000 = ₹2000

\text{Total Selling Price} = 1200 + 800 = ₹2000

Step 4: Calculate overall profit or loss

\text{Overall Profit/Loss} = \text{Total S.P.} - \text{Total C.P.} = 2000 - 2000 = ₹0

Since the total selling price equals the total cost price, there is no profit and no loss.

Answer: No profit, no loss (Option A)

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Q.356 Medium HCF and LCM

The ratio of two numbers is 4:5 and their HCF is 8. Find the numbers.

A 24 and 30

B 32 and 40

C 28 and 35

D 36 and 45

Correct Answer: B. 32 and 40

Explanation:

Let numbers be 4k and 5k. HCF = k = 8. So numbers are 32 and 40

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Q.357 Medium HCF and LCM

A pipe can fill a tank in 10 hours and another pipe can empty it in 15 hours. If both pipes are opened together, how long will it take to fill the tank?

A 20 hours

B 25 hours

C 30 hours

D 40 hours

Correct Answer: C. 30 hours

Explanation:

Filling rate = 1/10, Emptying rate = 1/15. Net rate = 1/10 - 1/15 = 3/30 - 2/30 = 1/30. Time = 30 hours

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Q.358 Medium HCF and LCM

A shopkeeper marks an article at ₹1500 and gives a 30% discount. What is the selling price? Later, he applies an additional 10% discount on the discounted price. What is the final price?

A ₹900

B ₹945

C ₹1000

D ₹1050

Correct Answer: B. ₹945

Explanation:

After 30% discount: 1500 × 0.7 = ₹1050. After additional 10%: 1050 × 0.9 = ₹945

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Q.359 Medium Profit and Loss

A manufacturer sells goods to a wholesaler at 20% profit. The wholesaler sells to a retailer at 25% profit. The retailer sells to the customer at 30% profit. If the customer pays ₹1,950, what is the manufacturer's cost price?

A ₹1,000

B ₹1,200

C ₹1,500

D ₹1,300

Correct Answer: A. ₹1,000

Explanation:

Let manufacturer's CP = x. Wholesaler's CP = 1.2x. Retailer's CP = 1.2x × 1.25 = 1.5x. Customer pays = 1.5x × 1.3 = 1.95x = 1,950. So x = 1,000.

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Q.360 Medium Profit and Loss

Two articles are sold for ₹1,200 each. One at 20% profit and the other at 20% loss. What is the overall loss/profit percentage?

A 4% loss

B 4% profit

C No loss no gain

D 5% loss

Correct Answer: A. 4% loss

Explanation:

Article 1: CP₁ = 1200/1.2 = ₹1,000. Article 2: CP₂ = 1200/0.8 = ₹1,500. Total CP = ₹2,500, Total SP = ₹2,400. Loss = 4%.

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