1)The difference between the local value and the face value of 7 in the numberal 32675149 is
a) 75142 b) 64851 c) 5149
d) 69993 e) None of these
(Local value of 7) - (Face value of 7)
= (70000 - 7) = 69993
2) By what least number 675 be multiplied to obtain a number which is a perfect cube?
a) 5 b) 6 c) 7
d) 8 e) None of these
675 = 5 × 5 × 3 × 3 × 3
To make it a perfect cube, it must be multiplied by 5.
3)The least prefect square, which is divisible by each of 21, 36 and 66 is:
a) 213444 b) 214344
c) 214434 d) 231444
e) None of these
LCM of 21, 36 and 66 = 2772
Now, 2772 = 2 × 2 × 3 × 3 × 7 × 11
To make it a perfect square, it must be multiplied by 7 × 11
So, required number = (2)2 × (3)2 × (7)2 × (11)2 = 213444
4) A grocer has a sale of Rs. 6435, Rs. 6927, Rs. 6855, Rs. 7230 and Rs. 6562 for 5 consecutive months. How much sale must he have in the sixth month so that he gets an average sale of Rs. 6500?
a) Rs. 4991 b) Rs.5991
c) Rs. 6001 d) Rs. 6991
e) None of these
Total sale for 5 months = Rs. (6435 + 6927 + 6855 + 7230 + 6562) = Rs. 34009.
Required sale = Rs.[(6500 x 6) - 34009]
= Rs.39000 – 34009
= Rs. 4991
5) The average weight of 8 person's increases by 2.5 kg when a new person comes in place of one of them weighing 65 kg. What might be the weight of the new person?
a) 76Kg b) 76.5Kg
c) 85Kg d) Data inadequate
e) None of these
Total weight increased = (8 × 2.5) kg = 20 kg.
Weight of new person = (65 + 20) kg = 85 kg.
6) The smallest number which when diminished by 7, is divisible by 12, 16, 18, 21 and 28 is
a) 1008 b) 1015 c) 1022
d) 1032 e) None of these
Required numbers = (LCM of 12, 16, 18, 21, 28) + 7
= 1008 + 7 = 1015
7) Find the greatest number that will divide 43, 91 and 183 so as to leave the same remained in each case.
a) 4 b) 7 c) 9
d) 13 e) None of these
Required number
= HCF of (91 - 43), (183 - 91) and (183 - 43)
= HCF of 48, 92 and 140 = 4
8) The ratio of length to width of a rectangular sheet of paper is 5 : 3. If the width of the sheet is 18 cm, find its length?
a) 10 cm b) 20 cm
c) 25 cm d) 30 cm
e) None of these
Let the length of sheet of paper be x cm. Then the ratio of length to
width = x : 18
Thus, x : 18 = 5 : 3
x × 3 = 18 × 5 x = 30
Hence the length of paper = 30 cm
9) The students in three classes are in the ratio of 2 : 3 : 4. If 40 students are added in each class, the ratio becomes 4 : 5 : 6. Find the total number of students in all the three classes is :
a) 270 b) 180 c) 126
d) 135 e) None of these
2x + 40 = 4y … (i)
3x + 40 = 5y …. (ii)
4x + 40 = 6y ….. (iii)
Therefore 2x = 40 x = 20
Hence, total number of students = 2x + 3x + 4x = 9x
= 9 × 20 = 180
10) Aman started a business investing Rs.70,000. Rakhi joined him after six months with an amount of Rs.1,05,000 and Sagar joined them with Rs.1.4 lakhs after another six months. The amount of profit earned should be distributed in what ratio among Aman, Rakhi and Sagar respectively, 3 years after Aman started the business?
a) 7 : 6 : 10 b) 12 : 15 : 16
c) 42 : 45 : 56
d) Cannot be determined
e) None of these
Aman : Rakhi : Sagar
= (70000×36) : (105000×30) : 1400 00×24) = 12 : 15 : 16
11) The ratio between the present ages of P and Q is 5 : 7 respectively. If the difference between Q’s present age and P’s age after 6 years is 2, what is the total of P’s and Q’s present ages?
a) 46 years b) 48 years
c) 52 years d) 56 years
e) None of these
Let the present ages of P and Q be 5x
years and 7x years respectively.
Then 7x - (5x + 6) = 2
2x = 8
x = 4
Required sum = 5x + 7x= 12x
= 12 × 4 = 48 years
12) My brother is 3 years elder to me. My father was 28 years of age when my sister was born while my mother was 26 years of age when I was born. If my sister was 4 years of age when my brother was born, then, what was the age of my father and mother respectively when my brother was born?
a) 32 yrs., 23 yrs. b) 32 yrs., 29 yrs.
c) 35yrs., 29 yrs. d) 35 yrs., 33 yrs.
e) None of these
Clearly, my mother was born 3 years
before I was born and 4 years after my sister was born.
So, father’s age when = (28 + 4)
Brother was born = 32 years
Mother’s age when brother was born = (26- 3) = 23 years
13) A fruit seller sells mangoes at the rate of Rs.9 per kg and thereby loses 20%. At what price per kg, he should have sold them to make a profit of 5%?
a) Rs.11.81 b) Rs.12
c) Rs.12.25
d) Rs.12.31 e) None of these
85 : 9 = 105 : x
x = [9 × 105 /80]
= Rs.11.81
Hence, S.P. per kg = Rs.11.81
20) 10 women can complete a work in 7days and 10 children take 14 days to complete the work. How many days will 5 women and 10 children take to complete the work?
a) 3 b) 5 c) 7
d) Data inadequate
e) None of these
1 woman’s 1 day’s work = 1/ 70
1 child’s 1 day’s work = 1 /140
(5 women + 10 children)’s day’s work
= [5/ 70 + 10 /140] = [ 1/ 14 + 1 /14] = 1/7
5 women and 10 children will complete the work in 7 days.
15) What is the sum of 100 terms of the series 1 - 2 + 3 - 4 + 5 - 6 + … ?
a) 100 b) 50 c) 550
d) Data inadequate
e) None of these
(1 - 2) + (3 - 4) + (5 - 6) + (7 - 8) + ….+ (99 - 100)
= (-1) + (-1) + (-1) + (-1) + …. 50 times = - 50
16) A man in a train notices that he can count 21 telephone posts in one minute. If they are known to be 50 meters apart, then at what speed is the train travelling?
a) 55km/hr b) 57km/hr
c) 60km/hr d) 63km/hr
e) None of these
Number of gaps between 21
telephone posts = 20
Distance travelled in 1 minute = (50 ×20) m
= 1000 m = 1 km.
Speed of the train travelling is = 60km./hr.
17) A goods train leaves a station at a certain time and at a fixed speed. After 6 hours, an express train leaves the same station and moves in the same direction at a uniform speed of 90 kmph. This train catches up the goods train in 4 hours. Find the speed of the goods train.
a) 60 kmph b) 36 kmph
c) 12 kmph d) 24 kmph
e) None of these
Let the speed of the goods train be x kmph.
Distance covered by goods train in 10 hours = Distance covered by express train in 4 hours
So, 10x = 4 × 90 or x = 36.
So, speed of goods train = 36 kmph
Answers
1.d 2.a 3.a 4.a 5.c
6.b 7.a 8.d 9.b 10.b
11.b 12.a 13.a 14.c 15.b
16.c 17.b