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,
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?
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?
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
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?
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?
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?