1.The average speed of a tractor is two–fifths the average speed of a car. The car covers 450 km in 6 hours. How much distance will the tractor cover in 8 hours?
(1) 210km
(2) 240 km
(3) 420km
(4) 480 km
2.The area of a square is four times the area of a rectangle. The length of the rectangle is 25 cm and its breadth is one cm less than one–fifth of its length. What is the perimeter of the square?
(1) 40 cm
(2) 60 cm
(3) 160 cm
(4) None of these
3.What value will be obtained if the square of 22 is subtracted from the cube of 12?
(1) 1244
(2) 1344
(3) 1454
(4) 1354
4.The marks of six boys in a group are 48, 59, 87, 37, 78 and 57. What are the average marks of all six boys?
(1) 62
(2) 64
(3) 61
(4) 63
5.The ratio of the present ages of Tarun and Varun is 3 : 7. After 4 years Varun’s age will be 39 years. What was Tarun’s age 4 years ago?
(1) 12 years
(2) 13 years
(3) 19 years
(4) None of these
6.The sum of five consecutive even numbers is equal to 170. What is the sum of the second largest number and the square of the smallest number amongst them together?
(1) 940
(2) 932
(3) 938
(4) 936
7.How many sacks are required for filling 1026 kg of rice if each sack is filled with 114 kg of rice?
(1) 19
(2) 15
(3) 7
(4) 9
8.Ravi consistently runs 350 metres every day except on Tuesdays when he runs 500 metres. How many kilometres will he run in two weeks? (In this question the week starts from Monday.)
(1) 4.5 km
(2) 4.8 km
(3) 5.2 km
(4) 5.4 km
9.The simple interest accrued in 3 years on a principal of `25,000 is three–twentieths the principal. What is the rate of simple interest pcpa?
(1) 5
(2) 4
(3) 6
(4) 3
10. Sumit purchased an item for Rs.6,500 and sold it at a gain of 24%. From that amount he purchased another item and sold it at a loss of 20%. What is his overall gain/loss?
(1) Loss of Rs.42
(2) Gain of Rs.42
(3) Loss of Rs.52
(4) Neither gain nor loss
Answers and Solution:
1.(2); Average speed of the car = = 75 km/h
Average speed of the tractor = 75 ×2/5 = 30 km/h
Distance covered by the tractor = 30 × 8 = 240 km
2.(4); Length of the rectangle = 25 cm
Breadth of the rectangle = 25/5 –1 = 4 cm
Area of the rectangle = 25 × 4 = 100 sq cm
Area of the square = 4 × 100 = 400 sq cm
Side of the square = 20 cm
Perimeter of the square = 4 × 20 = 80 cm
3.(1); (12)^3 – (22)^2 = 1728 – 484 = 1244
4.(3);
5.(4); Varun’s present age = 39 – 5 = 35 years
So, Tarun’s present age = 15 years
Tarun’s age 4 years ago = 11 years
6.(4); Let the numbers be x, x + 2, x + 4, x+6 and x + 8
According to the question,
x + x + 2 + x + 4 + x + 6 + x + 8=170
or 5x + 20 = 170
or x + 4 = 34
or x = 30.
Second largest No. = 30 + 6 = 36
Square of smallest No. = 900
Sum of these Nos. = 900 + 36 = 936
7.(4);
8.(3);
9.(1);I = 25000 ×3/20 = 3750, r = (3750*100)/75000 = 5%
10.(3); Second selling price = 6500 * 124/100 *80/100 = 6448
Loss => 6500 – 6448 = Rs. 52
Average speed of the tractor = 75 ×2/5 = 30 km/h
Distance covered by the tractor = 30 × 8 = 240 km
2.(4); Length of the rectangle = 25 cm
Breadth of the rectangle = 25/5 –1 = 4 cm
Area of the rectangle = 25 × 4 = 100 sq cm
Area of the square = 4 × 100 = 400 sq cm
Side of the square = 20 cm
Perimeter of the square = 4 × 20 = 80 cm
3.(1); (12)^3 – (22)^2 = 1728 – 484 = 1244
4.(3);
5.(4); Varun’s present age = 39 – 5 = 35 years
So, Tarun’s present age = 15 years
Tarun’s age 4 years ago = 11 years
6.(4); Let the numbers be x, x + 2, x + 4, x+6 and x + 8
According to the question,
x + x + 2 + x + 4 + x + 6 + x + 8=170
or 5x + 20 = 170
or x + 4 = 34
or x = 30.
Second largest No. = 30 + 6 = 36
Square of smallest No. = 900
Sum of these Nos. = 900 + 36 = 936
7.(4);
8.(3);
9.(1);I = 25000 ×3/20 = 3750, r = (3750*100)/75000 = 5%
10.(3); Second selling price = 6500 * 124/100 *80/100 = 6448
Loss => 6500 – 6448 = Rs. 52
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