Q: 50 men took a dip in a water tank 40 m long and 20 m broad on a religious day. If the average displacement of water by a man is 4 cu.m , then the rise in the water level in the tank will be:
Solution: Total volume of water displaced =(4 x 50) cu.m = 200 cu.m Rise in water level = 20040×20=0.25m = 25cm The correct answer is: B) 25 cm
Q: The product of two numbers is 4107. If the H.C.F of these numbers is 37, then the greater number is
Solution: Let the numbers be 37a and 37b. Then , 37a x 37b =4107 => ab = 3. Now co-primes with product 3 are (1,3) So, the required numbers are (37 x 1, 37 x 3) i.e, (37,111). Therefore, Greater number = 111. The correct answer is: C) 111
Q: The cost of Type 1 rice is Rs. 15 per kg and Type 2 rice is Rs.20 per kg. If both Type 1 and Type 2 are mixed in the ratio of 2 : 3, then the price per kg of the mixed variety of rice is
Solution: Let the price of the mixed variety be Rs. x per kg. By the rule of alligation, we have : Cost of 1 kg of type 1 rice Cost of 1 kg of type 2 rice ∴(20-x)/(x-15) = 2/3 ⇒ 60 - 3x = 2x - 30 ⇒ x = 18. The correct answer is: C) Rs. 18
Q: A man sitting in a train which is traveling at 50 kmph observes that a goods train, traveling in opposite direction, takes 9 seconds to pass him. If the goods train is 280 m long, find its speed.?
Solution: Relative speed =280/9 m / sec = (280/9*18/5) kmph = 112 kmph. Speed of goods train = (112 - 50) kmph = 62 kmph. The correct answer is: B) 62
Q: A can contains a mixture of two liquids A and B in the ratio 7 : 5. When 9 litres of mixture are drawn off and the can is filled with B, the ratio of A and B becomes 7 : 9. How many litres of liquid A was contained by the can initially?
Solution: Suppose the can initially contains 7x and 5x litres of mixtures A and B respectively Quantity of A in mixture left =7x-712×9=7x-214 litres. Quantity of B in mixture left = 5x-512×9=5x-154litres. 7x-2145x-154+9=79 ⇒28x-2120x+21=79 ⇒x=3 So, the can contained 21 litres of A. The correct answer is: C) 21
Q: Three unbiased coins are tossed.What is the probability of getting at least 2 heads? . Let E = event of getting at least two heads = {THH, HTH, HHT, HHH}. P(E) = n(E) / n(S) = 4/8= 1/2 }Solution: Here S= {TTT, TTH, THT, HTT, THH, HTH, HHT, HHH
The correct answer is: B) 1/2Q: A tank is 25m long 12m wide and 6m deep. The cost of plastering its walls and bottom at 75 paise per sq m is
Solution: Area to be plastered = 2l+b×h+l×b =225+12×6+25×12=744sq.m Cost of plastering = 744×75100=Rs.558 The correct answer is: D) Rs. 558
Q: A parallelogram has sides 30m and 14m and one of its diagonals is 40m long. Then its area is
Solution: let ABCD be the given parallelogram area of parallelogram ABCD = 2 x (area of triangle ABC) now a = 30m, b = 14m and c = 40m s=1/2 x (30+14+40) = 42 Area of triangle ABC = ss-as-bs-c = 4212282= 168sq m area of parallelogram ABCD = 2 x 168 = 336 sq m The correct answer is: C) 336
Q: A certain sum of money amounts to Rs 1008 in 2 years and to Rs 1164 in 3 ½ years. Find the sum and the rate of interest.
Solution: S.I. for 1 ½ years = Rs (1164 - 1008) = Rs 156 . S.I. for 2 years = Rs (156 x 23 x 2)= Rs 208. Therefore, Principal = Rs (1008 - 208) = Rs 800. Now, P = 800, T= 2 and S.I. = 208. Therefore, Rate = (100 x S.I.) / (P x T) = [ (100 x 208)/(800 x 2)]% = 13% The correct answer is: B) 800, 13%
Q: Product of two co-prime numbers is 117. Their L.C.M should be
Solution: H.C.F of co-prime numbers is 1. So, L.C.M = 117/1 =117 The correct answer is: B) 117
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