1.The distance between two stations A and B is 220 km. A train leaves A towards B at an average speed of 80 km/hr. After half a hour, another train leaves B towards A at an average speed of 100 km/hr. The distance of the point where the two trains meet, from A is :
(a) 120 km
(b) 130 km
(c) 140 km
(d) 150 km
Let required distance be x km. Then,
x/80−(220−x)/100=1/2
⇒5x−4(220−x)=200
⇒9x=1080
⇒x=120km
2.A cart has to cover a distance of 80 km in 10 hours. If it covers half of the journey in (3/5)th time, what should be its speed to cover the remaining distance in the time left ?
(a) 8 km/hr
(b) 20 km/hr
(c) 6.4 km/hr
(d) 10 km/hr.
Distance left = (12×80) km=40 km
Time left = [(1-35)×10]=25×10=4hrs
Speed required = (40÷4) km/hr= 10 km/hr.
3.The average age of 12 players of a team is 25 yr. If the captain’s age is included, the average age increases by 1 yr. The age of the captain is?
(a) 25 yr
(b) 38 yr
(c) 36 yr
(d) 26 yr
Total age of 12 players = 12 × 25 = 300 yr
Total age including captain = 13 × 26 = 338 yr
Age of the captain = 338 – 300 = 38 yr
4.If a sum of money is to be divided among A, B and C such that A’s share is equal to twice B’s share and B’s share is 4 times C’s share, then their shares are in the ratio?
(a) 1:2:4
(b) 1:4:1
(c) 8:4:1
(d) 2:4:1
According to question, A : B = 2: 1, B : C = 4 : 1
A : B: C = 8 : 4 : 1
5.A book seller bought 200 text books for Rs. 12000. He wanted to sell them at a profit so that he got 20 books free. At what profit per cent should he sell them?
(a) 10%
(b) 11%
(c) 11.5%
(d) 12%
Cost price of a book Rs 12000/200 = Rs 60
Total profit = Rs. 60 × 20 =Rs. 1200
Profit per cent = (1200*100)/12000 = 10%
6.A sum of Rs 731 is distributed among A, B and C, such that A receives 25% more than B and B receives 25% less than C. What is C’s share in the amount?
(a) Rs 172
(b) Rs 200
(c) Rs 262
(d) Rs 272
Let C’s share be Rs x.
Then, B gets =0.75 x.
A gets = 1.25×0.75x
x+0.75x+0.9375x=731
2.6875x=731
x=731⁄2.6875 =272
7.Three sets of English, Mathematics and Science books containing 336, 240, 96 books respectively have to be stacked in such a way that all the books are stored subject wise and the height of each stack is the same. Total number of stacks will be?
(a) 14
(b) 21
(c) 22
(d) 48
8.In an examination, 60% of the candidates passed in English and 70% of the candidates passed in Mathematics, but 20% failed in both of these subjects. If 2500 candidates passed in both the subjects, the number of candidates that appeared at the examination was?
(a) 3000
(b) 3500
(c) 4000
(d) 5000
Let the total number of candidates = x
Number of candidates passed in English = 0.6x
Number of candidates passed in Maths = 0.7x
Number of candidates failed in both subjects = 0.2x
Number of candidates passed in at least one subject= x – 0.2x = 0.8x
0.6x + 0.7x – 2500 = 0.8x
1.3x – 0.8x = 2500
0.5x = 2500
X = 5000
9.After measuring 120 m of a rope, it was discovered that the measuring meter rod was 3 cm longer. The true length of the rope measured is?
(a) 121 m 20 cm
(b) 123 m 60 cm
(c) 123 m
(d) 116 m 40 cm
The meter rod is 3 cm longer.
True length of rope = 120 m + 120 × 3 cm
= 120 m + 360 cm= 123 m 60 cm
10.The ratio of the number of boys and girls in a school is 3:2. If 20% of the boys and 30% of the girls are scholarship holders, then the percentage of students, who do not get scholarship is?
(a) 50
(b) 72
(c) 75
(d) 76
