Combined rate = 1/6 + 1/8 + 1/10 = 20/120 + 15/120 + 12/120 = 47/120. Time = 120/47 ≈ 2.73 hours
Let CP = 100. MP = 140. SP = 140 × 80/100 = 112. Profit = 12%
When two trains move 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
Speed is given in km/h; convert to m/s by multiplying by \(\frac{5}{18}\):
Step 2: Find relative speed (trains moving towards each other)
When trains move towards each other, relative speed is the sum:
Or more precisely: \(v_{\text{relative}} = \frac{25}{2} + \frac{50}{3} = \frac{75 + 100}{6} = \frac{175}{6} \text{ m/s}\]
Step 3: Find total distance to be covered
For the trains to completely cross each other, the combined distance equals the sum of their lengths:
Step 4: Calculate time to cross
Using \(t = \frac{d}{v}\):
Answer: The trains will take \(12\) seconds to cross each other. (Option B)
Let B = 100, A = 120. Difference = 20. Percentage less = (20/120) × 100 = 16.67%
A's rate = 1/18, B's rate = 1/12. B alone for 3 days = 3/12 = 1/4. Remaining = 3/4. Combined rate = 1/18 + 1/12 = 5/36. Time together = (3/4)/(5/36) = 27/5 = 5.4 ≈ 5 days
Combined rate = 1/6 + 1/8 + 1/12 = (4+3+2)/24 = 9/24 = 3/8. Time = 8/3 = 2.67 days ≈ 2.4 days. Actually 8/3 ≈ 2.67, but closest is 2.4. Let me recalculate: LCM(6,8,12) = 24. Rate = 4/24 + 3/24 + 2/24 = 9/24 = 3/8. Time = 8/3 ≈ 2.67. Answer should be close to this.
Let CP = 100. MP = 150. SP = 150 × 80/100 = 120. Profit = 20. Profit% = 20%.
A = P(1+r/100)^n. 14400 = 12000(1+r/100)^2. 1.2 = (1+r/100)^2. √1.2 ≈ 1.095. r ≈ 9.5%. Closest is 10%.
Relative speed = 40 + 50 = 90 km/h = 25 m/s. Total distance = 150 + 250 = 400m. Time = 400/25 = 16 seconds. Closest option is 18 seconds.
[Work rate problems require finding individual work rates, then combining them to find the time taken when working together.]
A completes 1/3 of work in 5 days, so we calculate how much work A does per day.
B completes 2/3 of work in 10 days, so we calculate how much work B does per day.
When working together, their rates add up to find the total work completed per day.
To complete 1 full work at a combined rate of 2/15 per day, divide total work by combined rate.
A can do
3
1
of the work in 5 days.
So, A’s one-day work:
5
1/3
=
15
1
B can do
3
2
of the work in 10 days.
So, B’s one-day work:
10
2/3
=
30
2
=
15
1
Together, one-day work:
15
1
+
15
1
=
15
2
Time taken to complete the whole work:
2/15
1
=
2
15
=7.5
Therefore, together they can complete the work in:
7.5 days
Answer: B) 7.5 days
