1. In a class of 60 students, the number of boys and girls participating in the annual sports is in the ratio 3 : 2 respectively. The number of girls not participating in the sports is 5 more than the number of boys not participating in the sports. If the number of boys participating in the sports is 15, then how many girls are there in the class ?
a) 20
b) 25
c) 30
d) None of these
Explanation: Let the number of boys and girls participating in sports be 3x and 2x respectively.
Then, 3x = 15 or x = 5.
So, number of girls participating in sports = 2x = 10.
Number of students not participating in sports = 60 - (15 + 10) = 35.
Let number of boys not participating in sports be y.
Then, number of girls not participating in sports = (35 -y).
Therefore (35 - y) = y + 5 ⇔ 2y ⇔ 30 ⇔ y = 15.
So, number of girls not participating in sports = (35 - 15) = 20.
Hence, total number of girls in the class = (10 + 20) = 30.
2. There are deer and peacocks in a zoo. By counting heads they are 80. The number of their legs is 200. How many peacocks are there ?
a) 20
b) 30
c) 50
d) 60
Explanation: Let x and y be the number of deer and peacocks in the zoo respectively. Then,
x + y = 80 ...(i) and
4x + 2y = 200 or 2x + y = 100 ...(ii)
Solving (i) and (ii), we get) x = 20, y = 60.
3. A man wears socks of two colours - Black and brown. He has altogether 20 black socks and 20 brown socks in a drawer. Supposing he has to take out the socks in the dark, how many must he take out to be sure that he has a matching pair ?
a) 3
b) 20
c) 39
d) None of these
Explanation: Since there are socks of only two colours, so two out of any three socks must always be of the same colour.
4. A motorist knows four different routes from Bristol to Birmingham. From Birmingham to Sheffield he knows three different routes and from Sheffield to Carlisle he knows two different routes. How many routes does he know from Bristol to Carlisle ?
a) 4
b) 8
c) 12
d) 24
Explanation: Total number of routes from Bristol to Carlisle = (4 x 3 x 2) = 24.
5. Mac has £ 3 more than Ken, but then Ken wins on the horses and trebles his money, so that he now has £ 2 more than the original amount of money that the two boys had between them. How much money did Mac and Ken have between them before Ken's win ?
a) £ 9
b) £ 11
c) £ 13
d) £ 15
Explanation: Let money with Ken = x. Then, money with Mac = x + £ 3.
Now, 3x = (x + x + £ 3) + £ 2 ⇔ x = £ 5.
Therefore Total money with Mac and Ken = 2x + £ 3 = £ 13.
6. The total of the ages of Amar, Akbar and Anthony is 80 years. What was the total of their ages three years ago ?
a) 71 years
b) 72 years
c) 74 years
d) 77 years
Explanation: Required sum = (80 - 3 x 3) years = (80 - 9) years = 71 years.
7. Two bus tickets from city A to B and three tickets from city A to C cost Rs. 77 but three tickets from city A to B and two tickets from city A to C cost Rs. 73. What are the fares for cities B and C from A ?
a) Rs. 4, Rs. 23
b) Rs. 13, Rs. 17
c) Rs. 15, Rs. 14
d) Rs. 17, Rs. 13
Explanation: Let Rs. x be the fare of city B from city A and Rs. y be the fare of city C from city A.
Then, 2x + 3y = 77 ...(i) and
3x + 2y = 73 ...(ii)
Multiplying (i) by 3 and (ii) by 2 and subtracting, we get: 5y = 85 or y = 17.
Putting y = 17 in (i), we get: x = 13.
8. An institute organised a fete and 1/5 of the girls and 1/8 of the boys participated in the same. What fraction of the total number of students took part in the fete ?
a) 2/13
b) 13/40
c) Data inadequate
d) None of these
Explanation: Data inadequate
9. A number of friends decided to go on a picnic and planned to spend Rs. 96 on eatables. Four of them, however, did not turn up. As a consequence, the remaining ones had to contribute Rs. 4 each extra. The number of those who attended the picnic was
a) 8
b) 12
c) 16
d) 24
Explanation:
10. A, B, C, D and E play a game of cards. A says to B, "If you give me three cards, you will have as many as E has and if I give you three cards, you will have as many as D has." A and B together have 10 cards more than what D and E together have. If B has two cards more than what C has and the total number of cards be 133, how many cards does B have ?
a) 22
b) 23
c) 25
d) 35
Explanation: Clearly, we have :
B - 3 = E ...(i)
B + 3 = D ...(ii)
A+B = D + E+10 ...(iii)
B = C + 2 ...(iv)
A+B + C + D + E= 133 ...(v)
From (i) and (ii), we have : 2 B = D + E ...(vi)
From (iii) and (vi), we have : A = B + 10 ...(vii)
Using (iv), (vi) and (vii) in (v), we get:
(B + 10) + B + (B - 2) + 2B = 133 ⇔ 5B = 125 ⇔ B = 25.