Govt. Exams
Entrance Exams
Rate = 1/12 + 1/15 - 1/20 = (5+4-3)/60 = 6/60 = 1/10. Time = 10 hours.
Let A's cost = x. B's cost = 1.2x. C's cost = 1.2x × 1.25 = 1.5x = 7500. x = 5000.
Work is proportional to number of men. If work increases by 50%, men needed = M × 1.5 = 1.5M.
Downstream speed = 12 + 3 = 15 km/h. Upstream speed = 12 - 3 = 9 km/h. Time = 90/15 + 90/9 = 6 + 10 = 16 hours. Hmm, should be 16 not 15. Let me verify: 90/15 = 6, 90/9 = 10. Total = 16 hours.
To find the difference between compound interest and simple interest, we calculate both separately using the given principal, rate, and time period.
Step 1: Calculate Simple Interest
Simple interest is calculated using the formula \(SI = \frac{P \times R \times T}{100}\), where \(P\) is principal, \(R\) is rate, and \(T\) is time.
Step 2: Calculate Compound Interest
Compound interest is found using \(A = P\left(1 + \frac{R}{100}\right)^T\), then \(CI = A - P\).
Step 3: Find the Difference
The difference between compound interest and simple interest is:
Answer: The difference is ₹32 (Option A)
A's rate : B's rate = 3:2. Let A's rate = 3x, B's rate = 2x. Combined = 5x = 1/10. So x = 1/50. A's rate = 3/50, time = 50/3 ≈ 16.67 days.
CP = 100 × 50 = ₹5000. SP = 80 × 75 + 20 × 40 = 6000 + 800 = ₹6800. Profit = 800. Profit% = 800/5000 × 100 = 16%. Closest is 10% or need to recalculate.
In 2 hours (A for 1 hour, then B for 1 hour): Net filling = 1/10 - 1/15 = (3-2)/30 = 1/30. To fill 30/30, we need 60 hours of 2-hour cycles = 30 cycles of 2 hours = 60 hours. Hmm, this doesn't match. Let me recalculate: Each 2-hour cycle = 1/30 filled. 30 cycles needed = 60 hours total. But option is 24. Let me verify the problem setup again with the given options.
Savings = 100 - 25 - 30 = 45%. If 45% = 9000, then 100% = 9000 × 100/45 = 20,000.
[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
