General Mathematics

Question: A man cycles round the boundary of a rectangular park at the rate of 12 kmph and completes one full round in 8 minutes. If the ratio between the length and breadth of the park be 3 : 2 then its area is :
A
`1536 m^2`

B
`15360 m^2`

C
`153600 m^2`

D
None

Note: Perimeter = Distance covered in 8 min. `= ((12000)/(60) xx 8) m` `= 1600 m.` Let length = 3x metres and breadth = 2x metres. Then,` = 2 (3x + 2x)` `= 1600 or x = 160` :. Length = 480 m and breadth = 320 m :. Area` = (480 xx 320) m^2` `= 153600 m^2`
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Question: One side of a rectangle is 8 metres long and its diagonal measures 17 metres. The area of the rectangle is :
A
`126 m^2`

B
`63 m^2`

C
`144.5 m^2`

D
`120 m^2`

Note: Other side` = sqrt((17)^2 - 8^2` `= sqrt(289) - 64` `= sqrt(225)` `= 15 m.` :. Area `= (15 xx 8) m^2` `= 120 m^2`
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Question: The area of a rectangle 108 m long is the same as that of a square having each side 72 m long. The width of the rectangle is :
A
`36 m`

B
`48 m`

C
`42 m`

D
`37.5 m`

Note: Let, breadth = x metres. Then, `108 xx x = 72 xx 72 or x` `= ((72 xx 72)/(108))` `= 48 m.`
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Question: The area of a square is 0.5 hectare. Its diagonal is :
A
`50 m`

B
`100 m`

C
`250 m`

D
`50sqrt(2)`

Note: Area` = (1/2 xx 10000) m^2` `= 5000 m^2` `:. 1/2 (Diagonal)` `= 5000 or (Diagonal) m^2` `= 10000.` = Diagonal` = sqrt(10000)` `= 100 m`
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Question: If the base of a rectangle is increased by `10%` and the area is unchanged then the corresponding altitude must be decreased by :
A
`10%`

B
`9 1/11%`

C
`11%`

D
`11 1/9%`

Note: Let, length = a & breadth = b. Then, area = ab. New length` = (110)/(100) a = (11a)/10.` Let new breadth = c. Then,` (11a)/10 xx c = ab or c = (10b)/11.` :. Decrease in breadth` = (b/11 xx 1/b xx 100)%` `= 9 1/11%`
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Question: If the base of a rectangle is increased by `10%` and the area is unchanged then the corresponding altitude must be decreased by :
A
`10%`

B
`9 1/11%`

C
`11%`

D
`11 1/9%`

Note: Let, length = a & breadth = b. Then, area = ab. New length` = (110)/(100) a = (11a)/10.` Let new breadth = c. Then,` (11a)/10 xx c = ab or c = (10b)/11.` :. Decrease in breadth` = (b/11 xx 1/b xx 100)%` `= 9 1/11%`
1. Report
Question: If the base of a rectangle is increased by `10%` and the area is unchanged then the corresponding altitude must be decreased by :
A
`10%`

B
`9 1/11%`

C
`11%`

D
`11 1/9%`

Note: Let, length = a & breadth = b. Then, area = ab. New length` = (110)/(100) a = (11a)/10.` Let new breadth = c. Then,` (11a)/10 xx c = ab or c = (10b)/11.` :. Decrease in breadth` = (b/11 xx 1/b xx 100)%` `= 9 1/11%`
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Question: A rectangle carpet has an area of 60 sq.m. If its diagonal and longer side together equal 5 times the shorter side, the length of the carpet is :
A
`5 m`

B
`12 m`

C
`13 m`

D
``14.5 m`

Note: Let, length = x metres and breadth = y metres. Then, xy = 60 and `sqrt(x^2 + y^2 + x = xy` :. xy = 60 and` (x^2 + y^2) = (5y - x^2)` or xy = 60 and` 24y^2 - 10xy = 0` `:. 24y^2 - 10 xx 60 = 0 or y^2` `= 25 or y = 5` `:. x = (60/5) m` = 12 m. So, length of the carpet = 12 m.
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Question: The number of square shared tin sheets of side 20 cm that can be cut off from a square tin sheet of side 1 metre, is :
A
5

B
10

C
25

D
20

Note: Number of sheets `= ((100 xx 100)/(20 xx 20))` `= 25`
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Question: The length and breadth of a square are increased by 40% and 30% respectively. The area of the resulting rectangle exceeds the area of the square by :
A
`35%`

B
`42%`

C
`62%`

D
`82%`

Note: Let side of the square be a. Then, area` = a^2`. New length` = ((140)/(100) a)` `= (7a)/5,` New breadth` = ((130)/(100) a)` `= (13a)/10.` New area` = (7a)/5 xx (13a)/10` `= (91a^2)/50` Increase in area` = (41/50 a^2 xx 1/a^2 xx 100)%` `= 82%`
1. Report

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Question: A man cycles round the boundary of a rectangular park at the rate of 12 kmph and completes one full round in 8 minutes. If the ratio between the length and breadth of the park be 3 : 2 then its area is :

Question: One side of a rectangle is 8 metres long and its diagonal measures 17 metres. The area of the rectangle is :

Question: The area of a rectangle 108 m long is the same as that of a square having each side 72 m long. The width of the rectangle is :

Question: The area of a square is 0.5 hectare. Its diagonal is :

Question: If the base of a rectangle is increased by `10%` and the area is unchanged then the corresponding altitude must be decreased by :

Question: If the base of a rectangle is increased by `10%` and the area is unchanged then the corresponding altitude must be decreased by :

Question: If the base of a rectangle is increased by `10%` and the area is unchanged then the corresponding altitude must be decreased by :

Question: A rectangle carpet has an area of 60 sq.m. If its diagonal and longer side together equal 5 times the shorter side, the length of the carpet is :

Question: The number of square shared tin sheets of side 20 cm that can be cut off from a square tin sheet of side 1 metre, is :

Question: The length and breadth of a square are increased by 40% and 30% respectively. The area of the resulting rectangle exceeds the area of the square by :