APPoliceSIMains2019ArithmeticandReasoning Related Question Answers
26. A milk vendor generally sells 3 Grades of milk. Grade I is pure milk with no water mixed in it, Grade II is a mixture of milk and water in the ratio 3:2 and Grade III is a mixture of milk and water in the ratio 2:3. On a particular day he has x liters of Grade I and 3 liters of Grade III milk and he got an order to supply 7 liters of Grade II milk. The minimum value ofx (in litres) required to prepare 7 Its of Grade H milk by mixing Grade I milk, Grade III milk and water, is
27. A business man buys two qualities A and B of a product at Rs. 120 per kg and Rs. 60 per kg respectively. He then mixes these two qualities and sells at Rs. 100 per kg. Then the percentage increase in the profit on a certain quantity of the mixture of A and B in the ratio 7:11 on the profit on the same quantity of the mixture of A and B in the ratio 1:1, is
28. A jar contains a mixture of 2 liquids A and B in the ratio 4:1. If 10 liters of mixture is taken out and 10 liters of liquid B is poured into the jar, the ratio becomes 2:3. The amount of liquid A contained in the jar initially is
29. The amount of water to be mixed with 32 liters of pure fruit juice so as to get 25% profit on selling the mixture at the cost price of the pure juice, (in liters) is
30. A vessel of capacity V liters can be filled by two taps A and B independently in $$\frac{1}{4}$$ hr and $$\frac{1}{6}$$ hr respectively. A tap C empties the full tank at the rate of 7 liters per min. If all the 3 taps are opened simultaneously, the full vessel is emptied in 120 min. Then V =
31. A pipe can fill an empty cistern with water in 5 hours. Due to leakage in its bottom, it takes 6 hours to fill the cistern. When the cistern is full, the time (in hours) in which it is emptied due to leakage is
32. Three pipes A, B, C have flow rates of 2 liters, y liters and 3 liters per minute, (2 < y < 3) respectively. The lowest and the highest flow rates of the pipes are decreased by a constant quantity x. If the reciprocals of the flow rates of A, B, C are in arithmetic progression both before and after the change, then x =
33. A swimming pool is fitted with 3 pipes A, B, C to fill the pool. A and B together can fill the pool in half the time that is required for C to fill the pool. B takes 20 hours more than the time required for A and 14 hours more than the time required for C to fill the pool. Then the time (in hours) required for all the 3 pipes together to fill the pool is
34. Mohan is thrice as efficient as Srinu and completes a work in 40 hours less than the time taken by Srinu. If both of them work together, the time (in hours) required to complete that work is
35. Two children A and B are playing a game. A can draw a picture in,30 minutes and B can erase it in 40 minutes. If A starts drawing, and if the drawing sheet is passed on to these two alternately for every one minute, then the time (in minutes) required to complete a picture for the first time is
36. 18 men and 12 women can complete a work in 18 days. A women takes twice as much time as a man to complete that work. Then the number of days required for 8 men to complete the same work is
37. A boy, a man and a woman can do a work independently in 72, 12 and 48 days respectively. The number of women required to assist 6 boys and a man to complete that work in 2 days is
38. 64 men working 8 hours a day plan to complete a piece of work in 9 days. After 5 days, they were able to complete only 40% of the work. The number of hours they should work per day so as to complete the remaining work in 4 more days is
39. Two friends A and B working together can complete a piece of work in 16 days. A alone can do the same work in 32 days. If A and B work on alternate days, starting with B, the time (days) in which the work can be completed is
41. The number of zeros at the end of the product $$1003 \times 1001 \times 999 \times...\times123$$ is
42. If A = $$2^{352} 5^{411} 3^{152}$$ ; B = $$2^{352} 5^{410} 3^{153}$$ ; C = $$2^{350} 5^{412} 3^{149}$$, and D = $$2^{353} 5^{409} 3^{150}$$ then the descending order of A, B, C, D is
43. The smallest 5 digit number which when divided by 7,11 and 21 leaves the remainder 3 in each case is
45. If the number obtained after subtracting x from 2035 leaves the same remainder 5 when it is divided by 9,10 and 15, then the smallest possible x is
47. Let A = {(a, b, c)/ $$c^2$$ = $$a^2 + b^2$$ }. If (3, 5, x), (y, 3, 7), (1, z, 5) are three elements of the set 'A' and the LCM of $$x^2, y^2, z^2$$ is $$p_1^{\alpha_1} p_2^{\alpha_2} p_3^{\alpha_3} p_4^{\alpha_4}$$ where $$p_1, p_2, p_3, p_4$$ are primes, then $$\frac{p_1 + p_2 + p_3 + p_4}{\alpha_1 + \alpha_2 + \alpha_3 + \alpha_4}$$ =
48. If the number of numbers between 100 and 1000 that are divisible by 11 is x, then the number of total divisors of x is
49. Match the items of the following lists.List - A List - B a) a, b are prime numbers i) LCM of $$a, b \leq ab$$b) a, b are composite numbers ii) Conjugate surds c) $$ 1.34 \overline{54}$$iii) Irrational numbers d) $$(\sqrt[3]{2} + 3\sqrt{5})(\sqrt[3]{2} - 3\sqrt{5})$$iv) Rational numbers v) Co-prime numbers Correct answer for a, b, c, d is
50. Let $$p_1, p_2, p_3$$ be prime numbers and $$\alpha, \beta, \gamma$$ be positive integers. If $$p_1^\alpha p_2^\beta p_3^\gamma$$ is a divisor of 34864764 lying between 100 and 200, then ($$p_1 + p_2 + p_3$$)($$\alpha + \beta + \gamma$$) =
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