Mathematics Mcqs

If each side of a square is increased by 50% the ratio of the area of the resulting square to the area of the given square is__________?

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If each side of a square is increased by 50% the ratio of the area of the resulting square to the area of the given square is__________?

A. 5:4
B. 9:4
C. 4:5
D. 4:9

Explanation:
Let original side be x metres, then area = x2 Sq.m
New side =(150% of x)m = (150/100 × x)m =(3x/2)m
New area =(3x/2 x 3x/2)m2 = 9×2/4 m2
Required ratio of area = 9×2/4 : x2 = 9:4

If the length of a rectangle is increased by 20% and it’s breadth is decreased by 20% then it area________?

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If the length of a rectangle is increased by 20% and it’s breadth is decreased by 20% then it area________?

A. Increased by 4%
B. decreased by 4%
C. Decreased by 1%
D. Remains unchanged

Explanation:
Let length = x metres and breadth = y metres, then area =(xy)
New length =(120/100x)m = 6x/5 m
New breadth =(80/100 y)m
New area =(6x/5 x 4y/5)m2 = (24/25 xy)m2
Decreased in area =(xy – 24/25 xy)m2= xy/25 m2
Decreased % =(xy/25 x 1/xy x 100)% = 4%

If the length and width of a rectangular grand are each increased by 20% then what would be the percent increase in the area of the garden?

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If the length and width of a rectangular grand are each increased by 20% then what would be the percent increase in the area of the garden?

A. 20%
B. 24%
C. 36%
D. 44%

Let length = x metres and breadth = y metres , then area =(xy)m2
New length = 120/100x (6x/5)m
New breadth = 120/100 y = 6y/5m
New area (6x/5 x 6y/5)m2 = (36/25 xy)m2
Increase in area = (36/25xy – xy)m2 = (11/25 xy)m2
Increase % = (11/25 xy x 1/xy x 100)% = 44%

The length of a rectangular plot is increased by 25%. To keep it’s area uncharged the width of the plot should be___________?

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The length of a rectangular plot is increased by 25%. To keep it’s area uncharged the width of the plot should be___________?

A. Kept unchanged
B. Increased by 25%
C. Increased by 20%
D. Reduced by 20%

Explanation:
Let the length be x metres and breadth be y metres
Then it’s area =(xy)m2
New length =(125/100 x)m =(5x/4)m.
Let the new breadth be 2 metres
Then xy 5x/4 x 2 => 2 = 4/5 y
Decreased in width =(y -4/5 y) = y/5 metres
Decreased % in width =(y/5 x 1/y x 100)% = 20%

The perimeter of a rectangle and square are 160m each. The area of the rectangle is less than that it’s square by 100cm meters. The less than that of the square by 100 sq.meters. the length of rectangle is___________?

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The perimeter of a rectangle and square are 160m each. The area of the rectangle is less than that it’s square by 100cm meters. The less than that of the square by 100 sq.meters. the length of rectangle is___________?

A. 30m
B. 40m
C. 50m
D. 60m
Explanation:
Each side of the square = 160/4m =40 cm
2(l+b) = 160
=> (l+b) = 80 (40) 2 –lb = 100
=> lb =(1600 – 100) = 1500 (l-b) 2 = (l+b) 2 – 4lb
= (80) 2 -4 x 1500 =(6400 -6000) = 400 (l-b) = 20
Therefore, l+b = 80, l-b =20
=> 2l =100
=> l= 50m

The diagonal of a square is 4√2cm. The diagonal is another square whose area is double that of the first square is__________?

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The diagonal of a square is 4√2cm. The diagonal is another square whose area is double that of the first square is__________?

A. 8cm
B. 8√2cm
C. 16cm
D. 4√2cm

Explanation:
Area of given square = ½ x (diagonal) 2 = 16cm2
Area of new square =(2 x 16)cm2 = 32cm2
Let the diagonal of 2nd squared be D cm
Then ½ x D2 = 32
=> D2 =64
=> D = 8 cm

The area of a rectangle is 12 sq.metres and it’s length is 3 times that of it’s breadth. What is the perimeter of the rectangle?

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The area of a rectangle is 12 sq.metres and it’s length is 3 times that of it’s breadth. What is the perimeter of the rectangle?

A. 14m
B. 18m
C. 4m
D. None of these

Explanation:
Let the breadth be x metres , then it’s length = 3x metres
=>3x × x =12
=> x2= 4
=> x =2 l=6m, b =2m
=> Perimeter = 2(6+2)m = 16m