west Bengal police math

1) If n is an integer, then (n-3)²-n² is always divisible by

2) The ratio of the sides of a triangle is 3 :4:5 and its perimeter is 96 metres. Find the area of the triangle in sq. metres

3) A railway train travels 66 km in 1½ hrs . Its speed in metre/min is

4) A square garden has fourteen posts along each side at equal interval

Find how many ma posts are there in all four sides.

5) The greatest of the numbers 0.16, √0.16, (0.16)² and 0.16 is

6) A box contains 384 coins. in it the ratio of 1 rupee coins, 50 paise coins and 25 paise coin is 2:3:7 the total value of the coin in the box is

7) Rs. 5625 is divided among A,B and C in such a way that A gets half of B and C while B gets ¼th of A and C.How much A gets more than B ?

8)

9) The mixture of water and sugar in a glass has ratio sugar:water = 2:7 and the ratio in another glass of same mixture is 3:11 , Which is sweeter?

10) The least number which being subtracted from 70031 will make the
remainder divisibly by 9 is

11) The least number that must be added to the least number of 5 digit so that the sum maybe exactly divisible by 6,8, 10 and 15 is

12) Two positive numbers are in the ratio 4:5 and their product is 1620.
The greater of the number is

13) The sum of the series 2+4+6+….+50 is

14) A hawker purchased oranges at the rate of 4 oranges in a rupee, but

he sells at the rate of 5 oranges ina rupee. His loss is

15) The simplified value of  1.29×1.29×1.29+2.71×2.71×2.71+12×1.29×2.71 is

16) Find the ratio of purchase price and the sell price sothat their is 16⅔% profit

17) The sum of the ages of the father and son after 6 years will be 44 . At present the sum is

18) A bucket half filed with water wrights 70 kg. When it’s ¼th is empty, I weights 80 kg. Find the weight of the bucket when its ⅖th is filled with water

19) A seller sells a radio with a profit of 5%.He earns 8% profit if it is sold
at a price or Rs. 24 more. The purchase price is

20) Ram, Rahim and Ratan invested Rs, 5000, Rs. 4000 and Rs. 3000

respectively in a business.Ratan earns Rs. 200 p.m. for its supervision. If

the total profit is Rs. 8400, then the total income of Ratan is

21)

22) Find the H.C.F and L.C.M of  1½ , 3/4 and 9/16

23) By selling an article for Rs 120 a person loses 20%. If the article is sold for Rs 180, What is the gain or loss % ?

24) What-sum of money is to be divided among 3 men in the ratio 3:45 so

that the third man receives Rs. 10 only.

25) Find the least number which being added to 2866 will make the sum divisible by 13

27)

28) A number is divided by 56 and a reminder 29 is left. when the same number is divided by 8, the reminder is

29) If a/2=b/5=c/8 then the value of (a-b-c)/b is

30) Divide Rs. 350 among A, B and C so that A’s share: B’s share =2:3 and B’s share: C’s share =4:5

31) To equal some of money where invested one at 4% and other at 4½% at the end of 6 years, the simple interest received from the latter exceeded that received from the former by Rs 21. Each sum was

32) If x is any positve intergerthen x(x+1)(2x+1)is always divisible by

33) 83÷7.5

_____________

2.321 – .098

34) The numbers which divide 80 in such a way that the sum of their reciprocals is 4/75 are

35) 50 men do a work in 12 days working 6 hours per day. If 60 men want to complete the double of the above work in 8 days, how many hours per day is to be worked by each man ?

36) A man travelled of his journey by car, by rail, and walked the remaining 1 km. how far dis he go  ?

37) A number when decreased by 10% becomes 30. Find the number…..

38) 2.The product of any four consecutive odd natural numbers increased by a number K is a perfect square. The value of K is

39) There are 30 students in a class. The average age of first 20 students is

11.2years and that of next 10 students is 12.7 years.The average age(in

years)of the students of whole class is

40) 25% of number is added to 30% of 150. If the result is 75, then the number is

41) A man retired from his service at the age of 60. He served for 3/5th

years of his retirement age. He joined his job at the age of

42) The sum and difference of two numbers 9⅝ and 4⅜ are respectively and find their product.

43) The average of 11 number is 10.9 . If the average of first six is 10.5 and that of the last six is 11.4 the 6th number is

44) A garrison of 1600 men is provisioned for 60 days. after 15 days 6 month leave the garrison . the remaining provisions will last for

45) Two pipes can fill a tank in 12 hours and 10 hours respectively and a third pipe can empty in 20 hours, if all the pipes are opened together, then the tank will be filled in

46) The Square root of the square root of 0.00000001 is

47) The least number divisible by any integer between 1 and 9 is

48) A tank is filled up by a pipe A in 5 minutes while it is emptied by a pipe
B in 10 minutes. When the tank is half-filled up two pipes are opened
simultaneously. Find the time required so that ¾th of the tank is filled up

49) A and B can do a piece of work in 30 days, which B and C can do in 40 days. If C alone can do the work in 60 days, in how many days A alone will do the same work ?

50) A man donated Rs 2000 from his savings of Rs 12755 to a school and the rest was distributed among his wife son and daughter in ratio 6:5:4 . The wife gets

51)

52) The greatest two digit number whose square root is an integer

53) A,B and C started a partnership business paying the capital amount of Rs. 6500, Rs.9100 and Rs. 5200 respectively. They equality distributed among themselves the two-third of the total sum of profit Rs. 14400 and each took the share of the remaining amount of profit in the ratio of the capital amount each had paid. what was the sum of money each partner received?

54)

55)

56) 280 oranges were divided among 50 boys and girls so that each boy gets 5 organges and each girl  7 oranges. The number of girls is….

57) The ratio of boys and girls of a schoolwith 504 students is 13:11. What will be the new ratio if 12 girls leave?

58) The average of the first four of five numbers is 26 that of the last four is
25. The difference of the first and last number is

59) A bag contain some 5 Re coins and 10 Re. coins. if the total number of coin is 80 and the total is Rs. 600, the number of 10 Re. coins is

60) A number is increased consecutively two times by 20% each. The

original number is actually increased by

61) The simplified value of 1.1 +(1.1)² +(1.1)³ is

62) The sum ofthe ages of the fatherand his son before 5 years is 44. The
sum of their present age is

63) A’s salary is 20% lower than B’s salary. How much percent is B’s salary higher than A’s ?

64) How long will a boy take to run round a square field of side 35 metres, if

he runs at the rate of 9 km/hr?

65) A and B togethercomplete a work in 3 days. After two days of their work leaves and the work is completed in next twO days. In how many days B alone completes the work?

66) An alloy contains zínc and copper in the ratio 5:3.The quantity of zinc to

be mixed with 16 kg of the alloy so that the ratio will be 2:1 is

67) The average of 8 numbers is 24 and the average of another 24 numbers is 8.The average of all the numbers is

68)

69) A did ¾th of a piece of work in 18days. B who is twice as good a workman
as A, completed the work. B worked for……

70) A man deposited Rs.2400 in a Bank at a simple interest of 5%per annum. If he wants to purchase an article of price Rs. 3000, how many years he is to wait?

71) If x <5, which one is true? 

72) The value of 0.12% of Rs. 180 is

73) The simplified value of 1.2+ (12)²+(12)³ is

74) Find a number which when multiplied by 13 is increased by 180

75) The first July of 1995 was the Saturday. The 1st April of 1996 was a

76) The value of (1+√2+√3) – 2√3 – 2√6 – 2√2 is

77) Ifthere is aloss of 12½% to sell a cycle, the ratio of the purchase price
and selling price is

78) A man bought a horse and a carriage for rupees 500 and sold the horse at a gain of 20% and the carriage at a loss of 10%, thus gaining 2% on his outlay. For how much was the horse bought  ?

79) Which one is correct?

80) A train runs with a speed of 50km/hr and a car moves along the opposite direction with a speed of 0.5km/min. Their relative velocity is

81) In a class 42% of the total strength reads English, 36% reads Mathematics and 15% reads both the subjects. The percentage of students who study neither English nor Mathematics is

82) Find the least number of candidates in an examination so that the

percentage of successful candidates should be 76.8%.

83) Two identical bottles A and B of sweet drinks contain sugar such that 30% of sugar in A is equal to 40% sugar in B. The ratio of sugar in the two bottles is

84) Express Rs. 25 as percentage of Rs. 75

85) 10 years before father’s age was 4⅓ time his son’s age,10 years after father’s age will be 2(3/7) time son’s age. Find the sum of the age of the father and son at present.

86) Among the following statements the correct

√5+√3>2√

87) The difference of the greatest and the least numbers of four digits formed by 8,0,0,3 is

88) 30% of A=.25 of B=⅕th of C, then A:B:C is

89) Average age of A and B is 9 years 4 months and that of Band C is 4 years 8months. How many years A is older than C?

90) Find the number between 400 and 500 which is divisible 12, 16,and 24

91) Two mixtures contain milk and water in the ratio 5:4 and 2:1 . Equal volumes of the mixtures are mixed together. The ratio of milk is to water in the resulting mixture is

92) The volume is increased by 10% when water is freezed to ice. if melted then it volume is decreased by

93) If A :B=2:3, B:C=5:4 and C:D=7:8, then A:D is

94) Find the greatest prime factor of 2431……

95) Product of two numbers is 1575 and their quotient is 7. What are the numbers?

96) The ratio of ages of two persons is 4:7 and one is 30 years older than the  other. Find the sum of their ages.

97) A person purchased a T.V. 20%less than the market price and sells it

at 20% more than the market price. What is his percentage profit?

98) A train moving with a speed of 54 km/hr. crosses 270 metre bridge in
30 seconds. Find the length of the train.

99) Find the maximum number of trees which can be planted 20 metres apart on the two sides of a straight road 1760 metres long.

100) The sum of all the number of 3 digits which can be formed by the digits 3, 0, 4 is…

101) The ratio of daily wages of two Workers is 4: 3 and one gets daily Rs

9 more than the other, what are their daily wages?

102) A businessman purchased 35 kg dal of Rs. 525 and sells it at the rate of Rs. 18 per kg. Then the rate of profit or loss is

103) The value of {(.87)³ +(13)³ +/.87 × .39)}^0.5 is

104) The average of the first four of five numbers is 40 and that of the last four numbers is 60.The difference of the last and the first number is

105) 35% of 135 is 45% of x. Then x is

106) Find the least integer when added to 512makes it a perfect square.

107) The greatest number lying between 200 and 300, which when divided
by 6, 8, and 9, leaves a remainder 5 in each case.

108) A man joined in his service at the age of 24 years and died during his service period. If he served for 4/7th of his life time, then he lived

109) The least number that must be subtracted from 3000 will make the result divisible by 7, 11 and 13

110) Acistern is Ced with water by an inlet pipe in 20 mins, While it becomes
empty in 30mins. by an outer. If both areopened simultaneously,the
cistern is filled in

111) If A :B=3:4, C:B=5:4, C:D=10:9, then A:B:C:D is

112) 4 men prepares 4 mats in 4 days. How many mats can be prepared by 200 men in 200 days ?

113) Find the sum 5.3+3.25+12.1

114) The sum and the difference and the two numbers are 135 and 21 respectively. The difference of their square is

115) The ratio of two numbers is 5:7 and their difference is 60, find the
numbers,

116) The greatest prime number of two digit is

117) 42 oranges are distributed among some boys and girls. if each boy gets 3 then each girl get 6 while each boy gets 5 then each girl gets 3. The number of girls is

118) An alloy of zinc and copper contains the metals in the ratio 5:3.The

quantity of zinc to be added to 16 kg.of the alloy so that the ratio of the

metal may be 3:1 is

119) Find the greatest and least of √6+√5, √3+2√2, √2+3

120) If 20% of A =30% of B =1/6th of C, then A:B:C is

121) Find the sum of prime factors of 561.

122) A general having 11025 men under him, arranges them into a solid squad. The number of men in the front row is

123) Find the square root of 5/80

124) The ratio of the purchase price and selling price is 4: 5. The net profit is….

125) Two numbers whose G.C.M.is 20 are in the ratio 3:4. Their sum is