21. Find the cost of fencing around a circular field of diameter 28 m at the rate of Rs1.50 a meter?
Answer: Rs 132.
Explanation:Formula: Area = (2 * pi * r)
Area of the field= 2 * 22/7 * 14 = 88 meter^2
So, the fencing cost = Rs 88 * 1.50 = Rs 132.
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22. In a covering a certain distance, the speeds of A and B are in the ratio of 3:4. A takes 30 minutes more than B to reach the destination. The time taken by A to reach the destination is?
Answer: 2 hours.
Explanation:As per the question:
Ratio of speeds = 3:4
Ratio of times taken = 4:3
Suppose A takes 4x hrs and B takes 3x hrs to reach the destination.
Then, 4x - 3x = 30/60 => x = 1/2
Time taken by A = 4x hrs = 4 * 1/2 = 2 hrs.
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23. A train 110 m long is running with a speed of 60 km/hr. In what time will it pass a man who is running at 6 km/hr in the direction opposite to that in which the train is going?
Answer: 6 sec.
Explanation:Relative speed = (60 + 6) = 66 km/hr.
converting km/hr to m/sec.
=> (66 * 5/18) = 55/3 m/sec.
Time required to pass the men = 110 * 3/55 = 6 sec.
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24. If the sum of the two numbers is 22 and the sum of their squares is 404, then the product of the numbers is ?
Answer: 40
Explanation:Let the numbers be x and y.
Then, (x + y) = 22 and x^2 + y^2 = 404
Now,
=> 2xy = (x + y)^2 - (x^2 + y^2)
=> 2xy= 22^2 - 404 = 484 - 404 = 80.
=> xy = 40
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25. Three pipes A, B and C can fill a tank from empty to full in 30 minutes, 20 minutes and 10 minutes respectively. When the tank is empty, all the three pipes are opened. A, B and C discharge chemical Exputions P, Q and R respectively. What is the proportion of Expution R in the liquid in the tank after 3 minutes?
Answer: 6/11
Explanation:Part filled by A in 1 min. = 1/30
Part filled by B in 1 min. = 1/20
and Part filled by C in 1 min. = 1/10
So, Part filled by (A + B + C) in 3 minutes = 3(1/30 + 1/20 + 1/10) = 11/20.
Part filled by C in 3 minutes = 3/10
Hence, the Required ratio = 3/10 * 20/11 = 6/11.
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26. The principal that amounts to Rs. 4913 in 3 years at 6 1/4 % per annum C.I. compounded annually, is?
Answer: Rs. 4096
Explanation:Formula: P = Amount / (1 + R/100)^n
Principal = [4913 / (1 + 25/(4 * 100))3]
=> 4913 * 16/17 * 16/17 * 16/17 = Rs. 4096
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27. A completes a work in 2 days, B in 4 days, C in 9 and D in 18 days. They form group of two such that difference is maximum between them to complete the work. What is difference in the number of days they complete that work?
Answer: 14/3
Explanation:If C and D form a pair and A and B form a pair the difference is maximum.
Now C and D together can complete the work = 9*189+189*189+18 = 6 days.
A and B together can complete the work = 2*42 + 42*42 + 4 = 4/3 days.
Difference = (6 - 4/3) = 14/3 days.
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28. A, B and C started a business with capitals of Rs 8000, Rs 10000 and Rs 12000 respectively. At the end of the year, the profit share of B is Rs 1500. The difference between the profit shares of A and C is?
Answer: Rs. 600
Explanation:As per the question:
Ratio of investments of A, B and C is 8000 : 10000 : 12000 = 4 : 5 : 6
Given, profit share of B = Rs. 1500
5 parts out of 15 parts = Rs. 1500
Difference between the profit share of (A,C) = 6 - 4 = 2 parts
So, required difference = 2/5 *(1500) = Rs 600
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29. A alone can do a piece of work in 6 days and B alone in 8 days. A and B undertook to do it for Rs 3200. With the help of C, they completed the work in 3 days. How much is to be paid to C?
Answer: Rs. 400
Explanation:A's 1 day work = 1/6
B's 1 day work = 1/8
So, C's 1 day's work = 1/3 - (1/6 + 1/8) = (1/3 - 7/24) = 1/24.
So, A's wages : B's wages : C's wages
=> 1/6 : 1/8 : 1/24 = 4:3:1
So, C's share = (1/8 * 3200) = Rs 400.
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30. I bought a book for Rs 60 , I sold off to a friend for Rs 70 but after a while i felt sorry , that i sold it and bought it back for Rs 80, how much loss did I incur?
Answer: Rs. 10
Explanation:Given, CP of the book = Rs. 60
And, SP of the book = Rs. 70
So, Profit = Rs. 10
Again, 2nd CP = Rs. 80
Hence, the total loss = (80 -70) = 10.
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