When two objects travel towards each other, their combined distance equals the sum of distances covered by each object individually.

The slower train covers 240 km in 4 hours, so we can calculate its speed directly.

The ratio of speeds is 3:4, where 3 represents the slower train and 4 represents the faster train.

When trains travel towards each other and meet, the sum of distances covered by both equals the total distance between stations.

The distance between the two stations is 560 km.

The ratio of speeds of the two trains is:

3:4

Let their speeds be:

3x km/h and 4x km/h

The slower train travels at 3x km/h and covers 240 km in 4 hours.

So,

3x×4=240

12x=240

x=20

Thus,

Slower train speed =3x=60 km/h

Faster train speed =4x=80 km/h

In 4 hours, the faster train covers:

80×4=320 km

Total distance between the stations:

240+320=560 km

Therefore, the distance between the two stations is:

560 km

​

The answer is (A) 560 km.

Let x be invested at 12%, (5000-x) at 8%. 0.12x + 0.08(5000-x) = 520. 0.12x + 400 - 0.08x = 520. 0.04x = 120. x = 3000. Wait, let me recalculate: 0.12x + 0.08(5000-x) = 520. 12x + 8(5000-x) = 52000. 12x + 40000 - 8x = 52000. 4x = 12000. x = 3000. So answer should be C, not A. But given answer is A=2000. Let me verify with A: 0.12(2000) + 0.08(3000) = 240 + 240 = 480 ≠ 520. With C: 0.12(3000) + 0.08(2000) = 360 + 160 = 520. ✓ Correct answer is C=3000.

CP per article = 4000/100 = 40. CP of 60 articles = 2400, SP = 2400 × 1.1 = 2640. CP of 40 articles = 1600, SP = 1600 × 0.95 = 1520. Total SP = 2640 + 1520 = 4160. Profit = 4160 - 4000 = 160. Profit% = (160/4000) × 100 = 4%. But answer is B=2%. Rechecking: this should give 4%, not 2%. Let me verify the calculation once more. If answer should be B, there may be different problem parameters.

Rate of pipe 1 = 1/15, Rate of pipe 2 = 1/20. Combined rate = 1/15 + 1/20 = 4/60 + 3/60 = 7/60. Time = 60/7 ≈ 8.57 minutes.

To find the final price after two successive percentage changes, apply each change sequentially to the original price.

Step 1: Calculate price after 25% increase in Year 1

Initial price = Rs. 1000

A 25% increase means the new price is 125% of the original:

\[

\text{Price after Year 1} = 1000 \times \frac{125}{100} = 1000 \times 1.25 = \text{Rs. } 1250

\]

Step 2: Calculate price after 20% decrease in Year 2

The price decreases by 20% from Rs. 1250, so the new price is 80% of the previous price:

\[

\text{Price after Year 2} = 1250 \times \frac{80}{100} = 1250 \times 0.80 = \text{Rs. } 1000

\]

Alternative approach (combined multiplier):

Apply both changes as a single operation:

\[

\text{Final Price} = 1000 \times 1.25 \times 0.80 = 1000 \times 1.00 = \text{Rs. } 1000

\]

Note that the multipliers \(1.25 \times 0.80 = 1.00\), meaning the two percentage changes exactly cancel out.

Answer: Rs. 1000 (Option C)

B's rate = 1/24. A is 50% more efficient, so A's rate = 1.5 × (1/24) = 1.5/24 = 1/16. A takes 16 days.

CP = 700. For 20% profit, SP = 700 × 1.2 = 840. After 30% discount, SP = 0.7 × MP. So 840 = 0.7 × MP. MP = 840/0.7 = 1200.

A = P(1.1)³ = 1.331P. Given A = 1331, so P = 1000

B's rate = 1/12 - 1/20 = (5-3)/60 = 2/60 = 1/30. B takes 30 days

After 10% discount: 800 × 0.9 = 720. After 15% discount: 720 × 0.85 = 612