1.The ratio of the areas
of two isosceles triangles having equal vertical angles is 1 : 4. The ratio of
their heights will be
(1) 1 : 2
(2) 3 : 4
(3) 2 : 3
(4) 6 : 7
2.If each of the radius of base and height of a right circular cone is increased by 10%, then the percentage of increase in the volume of the cone will be
(1) 20
(2) 33. 1
(3) 44.2
(4) 100
3.While selling a shirt, a shopkeeper gives a discount of 7%. If he had given a discount of 9% he would have got Rs. 15 less as profit. The marked price of the shirt is
(1) Rs. 750
(2) Rs. 720
(3) Rs. 712.50
(4) Rs. 600
4. A person went from A to B at an average speed of x km/hr and returned from B to A at an average speed of y km/hr. What was his average speed during the total journey?
(1) x + y/2xy
(2) 2xy/x + y
(3) 2/x+y
(4) 1/x + 1/y
5. The average monthly salary of A and B is Rs. 14000, that of B and C is Rs. 15600, and that of A and C is Rs. 14400. Monthly salary of B is
(1) Rs. 12400
(2) Rs. 12800
(3) Rs. 15200
(4) Rs. 16000
6. In an examination 42% students failed in Hindi and 52% failed in English. If 17% failed in both of these subjects, the percentage of students who passed in both the subjects, was
(1) 23
(2) 27
(3) 34
(4) 40
7.A reduction of 20% in the price of apples enables a man to buy 16 kg more apples for Rs. 4000. What is the reduced price per kg of apples?
(1) Rs. 64
(2) Rs. 60
(3) Rs. 50
(4) Rs. 40
8. Two numbers are less than a third number by 30% and 37% respectively. The per cent by which the second number is less than the first is
(1) 10
(2) 7
(3) 4
(4) 3
9. A is twice as fast runner as B, and B is thrice as fast runner as C. If C travelled a distance in 1 hour 54 minutes, the time taken by B to cover the same distance is
(1) 19 minutes
(2) 38 minutes
(3) 51 minutes
(4) 57 minutes
10.A lent Rs. 5000 to B for 2 years and Rs. 3000 to C for 4 years at simple interest at the same rate of interest. He received Rs. 2200, in all, from both of them as interest. The rate of interest perannum was
(1) 5%
(2) 7%
(3) 8%
(4) 10%
ANSWERS AND SOLUTION:
1.(1) The areas of two similar triangles are in the ratio of square of their corresponding altitudes.
2.(2) Volume of the cone = 1/3 πr^2 h
Effective change of 10% and 10% =
= {10 + 10 + (10 * 10)/100} = 21%
Effective change of 21% and 10%
= {21 + 10 + (21 * 10)/100}% = 33.1%
3.(1) Let the marked price of the shirt be Rs. x.
Difference of discounts = 2%
SO 2% of x = 15
=>(x * 2)/100 = 15
=> x = (15 * 100)/2 = Rs. 750
4.(2)
5.(3) A + B + C = Rs. 2/2 (14000 + 15600 + 14400) = Rs. 44000
A + C = Rs. (2 * 14400)
= Rs. 28800
SO B = Rs. (44000 – 28800)
= Rs. 15200
6.(1) Percentage of students who failed in Hindi or English or both = 42 + 52 – 17 = 77%
SO Percentage of students who passed
= 100 – 77 = 23%
7.(3) let the original price of apple = Rs. x per kg
New price = Rs. 4x/5
SO 4000 * 5 /4x – 4000/x = 16
=>1000/x = 16
=>X = 1000/16 = 62.5
SO New price = 4/5x
= Rs. (4/5 * 62.5)
New price = 4/5x
= Rs. 50 per kg
8.(1) Third number = 100
First number = 70
Second number = 63
SO Required percentage = 7/70 * 100 = 10
9.(2) Ratio of the speeds of A and B
= A : B = 2 : 1 = 6 : 3
B : C = 3 : 1
so A : B : C = 6 : 3 : 1
Ratio of their time taken
=1/6 : 1/3 : 1
so Time taken by B
= (2/6 * 114) minutes
= 38 minutes
10.(4) (5000 * 2 * R)/100 + (3000 * 4 * R) /100
= 2200
= 100R + 120R = 2200
= 220R = 2200
= R = 2200/220 = 10%
(2) 3 : 4
(3) 2 : 3
(4) 6 : 7
2.If each of the radius of base and height of a right circular cone is increased by 10%, then the percentage of increase in the volume of the cone will be
(1) 20
(2) 33. 1
(3) 44.2
(4) 100
3.While selling a shirt, a shopkeeper gives a discount of 7%. If he had given a discount of 9% he would have got Rs. 15 less as profit. The marked price of the shirt is
(1) Rs. 750
(2) Rs. 720
(3) Rs. 712.50
(4) Rs. 600
4. A person went from A to B at an average speed of x km/hr and returned from B to A at an average speed of y km/hr. What was his average speed during the total journey?
(1) x + y/2xy
(2) 2xy/x + y
(3) 2/x+y
(4) 1/x + 1/y
5. The average monthly salary of A and B is Rs. 14000, that of B and C is Rs. 15600, and that of A and C is Rs. 14400. Monthly salary of B is
(1) Rs. 12400
(2) Rs. 12800
(3) Rs. 15200
(4) Rs. 16000
6. In an examination 42% students failed in Hindi and 52% failed in English. If 17% failed in both of these subjects, the percentage of students who passed in both the subjects, was
(1) 23
(2) 27
(3) 34
(4) 40
7.A reduction of 20% in the price of apples enables a man to buy 16 kg more apples for Rs. 4000. What is the reduced price per kg of apples?
(1) Rs. 64
(2) Rs. 60
(3) Rs. 50
(4) Rs. 40
8. Two numbers are less than a third number by 30% and 37% respectively. The per cent by which the second number is less than the first is
(1) 10
(2) 7
(3) 4
(4) 3
9. A is twice as fast runner as B, and B is thrice as fast runner as C. If C travelled a distance in 1 hour 54 minutes, the time taken by B to cover the same distance is
(1) 19 minutes
(2) 38 minutes
(3) 51 minutes
(4) 57 minutes
10.A lent Rs. 5000 to B for 2 years and Rs. 3000 to C for 4 years at simple interest at the same rate of interest. He received Rs. 2200, in all, from both of them as interest. The rate of interest perannum was
(1) 5%
(2) 7%
(3) 8%
(4) 10%
ANSWERS AND SOLUTION:
1.(1) The areas of two similar triangles are in the ratio of square of their corresponding altitudes.
2.(2) Volume of the cone = 1/3 πr^2 h
Effective change of 10% and 10% =
= {10 + 10 + (10 * 10)/100} = 21%
Effective change of 21% and 10%
= {21 + 10 + (21 * 10)/100}% = 33.1%
3.(1) Let the marked price of the shirt be Rs. x.
Difference of discounts = 2%
SO 2% of x = 15
=>(x * 2)/100 = 15
=> x = (15 * 100)/2 = Rs. 750
4.(2)
5.(3) A + B + C = Rs. 2/2 (14000 + 15600 + 14400) = Rs. 44000
A + C = Rs. (2 * 14400)
= Rs. 28800
SO B = Rs. (44000 – 28800)
= Rs. 15200
6.(1) Percentage of students who failed in Hindi or English or both = 42 + 52 – 17 = 77%
SO Percentage of students who passed
= 100 – 77 = 23%
7.(3) let the original price of apple = Rs. x per kg
New price = Rs. 4x/5
SO 4000 * 5 /4x – 4000/x = 16
=>1000/x = 16
=>X = 1000/16 = 62.5
SO New price = 4/5x
= Rs. (4/5 * 62.5)
New price = 4/5x
= Rs. 50 per kg
8.(1) Third number = 100
First number = 70
Second number = 63
SO Required percentage = 7/70 * 100 = 10
9.(2) Ratio of the speeds of A and B
= A : B = 2 : 1 = 6 : 3
B : C = 3 : 1
so A : B : C = 6 : 3 : 1
Ratio of their time taken
=1/6 : 1/3 : 1
so Time taken by B
= (2/6 * 114) minutes
= 38 minutes
10.(4) (5000 * 2 * R)/100 + (3000 * 4 * R) /100
= 2200
= 100R + 120R = 2200
= 220R = 2200
= R = 2200/220 = 10%
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