Decode percentage of change in area of these shapes

Hyderabad: This article is in continuation to the last article focusing on the percentage topic. Here are some practice questions along with solutions that will help you in your preparation for the State government recruitment jobs. 1. If the area of a square is decreased by 36%, then the diagonal of a square is decreased […]

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

1. If the area of a square is decreased by 36%, then the diagonal of a square is decreased by?
a) 20% b) 22.5% c) 25% d) 27.5%
Ans: a

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Solution: 36% = -36/100
Area = (diagonal)2/2
Area = 100 : 64
Side = 10 : 8
– 2/10 × 100% = – 20%

2. If the length and breadth of a rectangle are increased by 10% and 8% respectively, then by how much percentage will the area increase?
a) 18.8% b) 19.8% c) 17.8% d) 18%
Ans: a

Solution: 10% = 10/100 = 1/10, 8% = 8/100 = 2/25
Area = length × breadth
Length —>; 10 : 11
Breadth —>; 25 : 27
Area —>; 10 × 25 : 11 × 27
250 : 297
47/ 250 × 100% = 18.8%

3. The length and breadth of a rectangle are doubled, then the percentage increase in the area is?
a) 100% b) 200% c) 300% d) 400%
Ans: c

Solution: Area = length × breadth
Length —>; 1 : 2
Breadth —>; 1 : 2
Area —>; 1 : 4
3/1 × 100% = 300%

4. If the length of a rectangle is increased by 20% and breadth is decreased by 20%, its area will be?

a) 2% increase b) 4% increase c) 4% decrease d) No change in its area
Ans: c

Solution: 20% = 20/100 = 1/5, 20% = -20/100 = -1/5
Length —>; 5 : 6
Breadth —>; 5 : 4
Area —>; 25 : 24
-1/25 × 100% = – 4%

5. The length of a rectangle is increased by 60%, then by what percent should the breadth be decreased to maintain the same area?
a) 60% b) 120% c) 75% d) 37 1/2%
Ans: d

Solution: 60% = 60/100 = 3/5
Length —>; 5 : 8
Breadth —>; 8 : 5 (Area remains same)
-3/8 × 100% = -37 1/2%

6. The initial length of a rectangular box is 20cm. This box is remade such that its length is increased by 30% but its breadth is decreased by 20%. If the area is increased by 100 cm², then find new area of box.
a) 2500 sq.cm b) 2600 sq.cm c) 2550 sq.cm d) 2650 sq.cm
Ans: b

Solution: 30% = 30/100 = 3/10, 20% = -20/100 = -1/5
Area = length × breadth
Length —>; 10 : 13
Breadth —>; 5 : 4
Area —>; 50 : 52
25 : 26
1 —>; 100 cm²
26 —>; ?
26 × 100 = 2600 sq.cm

7. If the radius of a circle is increased by 50%, its area is increased by?
a) 50% b) 75% c) 100% d) 125%
Ans: d

Solution: 50% = 50/100 = 1/2
Area = Pi r2
Radius —>; 2 : 3
Area —>; 2² : 3²
4 : 9
5/4 × 100% = 125%

8. If the radius of a circle is decreased by 20%, its area is decreased by?
a) 20% b) 40% c) 36% d) 15%
Ans: c

Solution: 20% = -20/100 = -1/5
Area = pi r2
Radius —>; 5 : 4
Area —>; 25 : 16
-9/25 × 100% = – 36%

To be continued…

M.Venkat
Director
MVK Publications
Dilsukhnagar
7671002120