Q1. A square and a rectangle have equal areas. If their perimeters are p_1 and p_2 respectively, then:
Q2. ABC is a right-angled triangle with right angle at B. If the semi-circle on AB with AB as diameter encloses an area of 81 sq. cm and the semi-circle on BC with BC as diameter encloses an area of 36 sq. cm, then the area of the semi-circle on AC with AC as diameter will be:
(a) 117 cm^2
(b) 121 cm^2
(c) 217 cm^2
(d) 221 cm^2
Q3. The difference between the circumference and the radius of a circle is 37 cm. The area of the circle is:
(a) 111 cm^2
(b) 148 cm^2
(c) 154 cm^2
(d) 259 cm^2
Q4. 2 metres broad pathway is to be constructed around a rectangular plot on the inside. The area of the plot is 96 sq. m. The rate of construction is Rs. 50 per square metre. Find the total cost of the construction
(a) Rs. 2400
(b) Rs. 4000
(c) Rs. 4800
(d) Data inadequate
Q5. The length of a blackboard is 8 cm more than its breadth. If the length is increased by 7 cm and breadth is decreased by 4 cm, the area remains the same. The length and breadth of the blackboard (in cm) will be:
(a) 28, 20
(b) 34, 26
(c) 40, 32
(d) 56, 48
Q6. A milk vendor has 2 cans of milk. The first contains 25% water and the rest is milk. The second contains 50% water. How much milk should he mix from each of the containers so as to get 12 litres of milk such that the ratio of water to milk is 3 : 5?
(a) 4 litres, 8 litres
(b) 6 litres, 6 litres
(c) 5 litres, 7 litres
(d) 7 lites, 5 litres
Q7. The cost of Type 1 rice is Rs. 15 per kg and Type 2 rice is Rs. 20 per kg. If both Type 1 and Type 2 are mixed in the ratio of 2 : 3, then the price per kg of the mixed variety of rice is:
(a) Rs. 18
(b) Rs. 18.50
(c) Rs. 19
(d) Rs. 19.50
Q8. The speed of a boat in still water is 10 km/hr. If it can travel 26 km downstream and 14 km upstream in the same time, the speed of the stream is:
(a) 2 km/hr
(b) 2.5 km/hr
(c) 3 km/hr
(d) 4 km/hr
Q9. Speed of a boat in standing water is 9 kmph and the speed of the stream is 1.5 kmph. A man rows to a place at a distance of 105 km and comes back to the starting point. The total time taken by him is:
(a) 16 hours
(b) 18 hours
(c) 20 hours
(d) 24 hours
Q10. The distance between two cities A and B is 330 km. A train starts from A at 8 a.m. and travels towards B at 60 km/hr. Another train starts from B at 9 a.m. and travels towards A at 75 km/hr. At what time do they meet?
(a) 10 a.m.
(b) 10.30 a.m.
(c) 11 a.m.
(d) 11.30 a.m.
Q11. A, B and C are on trip by a car. A drives during the first hour at an average speed of 50 km/hr. B drives during the next 2 hours at an average speed of 48 km/hr. C drives for the next 3 hours at an average speed of 52 km/hr. They reached their destination after exactly 6 hours. Their mean speed was:
(a) 50 km/hr
(b) 501/3 km/hr
(c) 511/3 km/hr
(d) 52 km/hr
Q12. Two workers A and B are engaged to do a work. A working alone takes 8 hours more to complete the job than if both worked together. If B worked alone, he would need 41/2 hours more to complete the job than they both working together. What time would they take to do the work together?
(a) 4 hours
(b) 5 hours
(c) 6 hours
(d) 7 hours
Q13. A and B can do a work in 8 days, B and C can do the same work in 12 days. A, B and C together can finish it in 6 days. A and C together will to it in:
(a) 4 days
(b) 6 days
(c) 8 days
(d) 12 days
Q14. A, B and C started a shop by investing Rs. 27,000, Rs. 72,000 and Rs. 81,000 respectively. At the end of the year, the profits were distributed among them. If C’s share of profit be Rs. 36,000, then the total profit was:
(a) Rs. 80,000
(b) Rs. 95,600
(c) Rs. 1,08,000
(d) Rs. 1,16,000
Q15. A, B, C started a business with their investments in the ratio 1 : 3 : 5. After 4 months, A invested the same amount as before and B as well as C withdrew half of their investments. The ratio of their profits at the end of the year is:
(a) 4 : 3 : 5
(b) 5 : 6 : 10
(c) 6 : 5 : 10
(d) 10 : 5 : 6
