Decode the percentage of shapes and sizes

Hyderabad: This article is in continuation to the last article focusing on the percentage topic. Here are some practice questions along with solutions on the percentage topic that will help you in your preparation for the State government recruitment jobs. 1. If the altitude of a triangle is increased by 20% and base is increased […]

Hyderabad: This article is in continuation to the last article focusing on the percentage topic. Here are some practice questions along with solutions on the percentage topic that will help you in your preparation for the State government recruitment jobs.

1. If the altitude of a triangle is increased by 20% and base is increased by 25%, then find the percentage increase in the area of a triangle?
a) 50% b) 45% c) 5% d) 22 1/2%

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Ans: a
Solution: 20% = 20/100 = 1/5, 25% = 1/100 = 1/4
Area = 1/2 × base × height
Height –>; 5 : 6, Base –>; 4 : 5
Area = 20 : 30
10/20 × 100% = 50%

2. If the altitude of a triangle is decreased by 10% and base is decreased by 20%, then find the percentage decrease in the area of a triangle?

a) 10% b) 15% c) 20% d) 28%

Ans: d

Solution: 10% = -10/100 = -1/10, 20% = -20/100 = -1/5
Altitude –>; 10 : 9 , Height –>; 5 : 4
Area = 1/2 × base × height
Area = 50 : 36
-14/50 × 100 = -28%

3. If the base of a triangle is decreased by 30% and height is increased by 10%, then find the percentage increase/decrease in the area of a triangle?
a) 23% increase b) 23% decrease c) 13% increase d) 13% decrease

Ans: b

Solution: 30% = -30/100 = -3/100, 10% = 10/100 = 1/10
Base –>; 10 : 7, Height –>; 10 : 11
Area = 1/2 × base × height
Area = 100 : 77
-23/100 × 100%
= 23% decrease

4. If the base of a triangle is increased by 25% and height is decreased by 20%, then find the percentage increase/decrease in area of a triangle?

a) 5% increase b) 5% decrease c) 22.5% increase d) No change

Ans: d

Solution: 25% = 25/100 = 1/4 , 20% = -20/100 = – 1/5
Area = 1/2 × base × height
Base –>; 4 : 5, Height –>; 5 : 4
Area = 20 : 20
0
= No change
5. If the altitude of a triangle is increased by 10% while its area remains same, its corresponding base will have to be decreased by?

a) 9% b) 10% c) 11 1/9% d) 9 1/11%

Ans: d
Solution: 10% = 10/100 = 1/10

Altitude –>; 10 : 11 , Base –>; 11 : 10 (area remains same)

11 : 10

-1/11 × 100 = -9 1/11%

6. If each side of a square is increased by 10%, its area will be increased by?

a) 100% b) 44% c) 21% d) 10%

Ans: c
Solution: 10% = 10/100 = 1/10

Area = side × side

Side –>; 10 : 11

10² : 11²

100 : 121
21/100 × 100% = 21%
7. If each side of a square is decreased by 25%, its area will be decreased by?

a) 43% b) 43.5% c) 43.75% d) 42.5%

Ans: c
Solution: 25% = -25/100 = -1/4

Area = Side × Side

Side –>; 4 : 3

4² : 3²

16 : 9
-7/16 × 100% = – 43.75%
8. If the diagonal of a square is increased by 20%, find the percentage increase in its area?

a) 20% b) 24% c) 40% d) 44%

Ans: d
Solution: 20% = 20/100 = 1/5
Area = (diagonal)2/2
Diagonal –>; 5 : 6
Area –>; 25 : 36
11/25 × 100% = 44%
9. If the diagonal of a square is decreased by 45%, find the percentage decrease in its area?

a) 69% b) 69.5% c) 69.75% d) 69.95%

Ans: c
Solution: 45% = – 45/100 = -9/20

Area = (diagonal)2/2

Diagonal –>; 20 : 11

Area –>; 400 : 121

-279/400 × 100% = – 69.75%

10. If the area of a square is increased by 21%, then the side of a square is increased by?
a) 10% b) 10.5% c) 12% d) 12.5%
Ans: a

Solution: 21% = 21/100
Area = 100 : 121
Side = 10 : 11
1/10 × 100% = 10%
11. If the area of a square is decreased by 19%, then the side of a square is decreased by?

a) 10.25% b) 10% c) 10.5% d) 10.75%

Ans: b
Solution: 19% = -19/100

Area = 100 : 81

Side = 10 : 9

-1/10 × 100% = – 10%

12. If the area of a square is increased by 44%, then the diagonal of a square is increased by?
a) 10% b) 15% c) 20% d) 22%
Ans: c

Solution: 44% = 44/100

Area = (diagonal)2/2

Area = 100 : 144

diagonal = 10 : 12

2/10 × 100% = 20%

To be continued

M.Venkat

Director
MVK Publications
Dilsukhnagar
7671002120