General Mathematics

Question: The cost of carpeting a room 18 m long with a carpet 75 cm wide at 45 paise per metre is Rs. 81. The breadth of the room is :
A
7 m

B
7.5 m

C
8 m

D
8.5 m

Note: Length of the carpet` = (Total Cost/Rate/m)` ` = (8100/450) m` ` = 180 m` Area of the room` = (180 xx 75/100) m^2` ` = 135 m^2` :. Area of the room` = Area of the carpet = 135 m^2` :. Breadth of the room` = (Area/Length)` ` = (135/18) m^2` ` = 7.5 m.`
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Question: A rectangular lawn 55 m by 35 m has two roads each 4 m wide running in the middle of it, one parallel to length and the other parallel to breadth. The cost of gravelling the roads at 75 paise per sq. metre is :
A
`Rs. 270`

B
`Rs. 262.50`

C
`Rs. 258`

D
`Rs. 254.50`

Note: Area of cross roads` = (55 xx 4 + 35 xx 4 - 4 xx 4) m^2` `= 344 m^2` :. cost of gravelling`= Rs. (344 xx 75/100)` `= Rs. 258`
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Question: A rectangular field has dimensions 25 m by 15 m. Two mutually perpendicular passages, 2 m wide have been left in the central part. In rest of the fields, grass has bee grown. The area under the grass is :
A
`295 m^2`

B
`299 m^2`

C
`300 m^2`

D
`375 m^2`

Note: Area of cross roads` = (25 xx 2 + 15 xx 2 - 2 xx 2) m^2` `= 76 m^2` Area of the field` = (25 xx 15) m^2` `= 375 m^2` Area under grass` = (375 - 76) m^2` `= 299 m^2`
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Question: The ratio between the length and breadth of a rectangular field is 5 : 4. If the breadth is 20 m less than the length, the perimeter of the field is :
A
`260 m`

B
`280 m`

C
`360 m`

D
None

Note: Let length = 5x and breadth = 4x in mertres. Then, `5x - 4x = 20 => x = 20` :. Length` = 100 m & Breadth = 80 m.` :. Perimeter` = 2 (100 + 80) m = 360 m.`
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Question: The length and breadth of a rectangular piece of land are in the ratio of 5 : 4 : 3. The owner spent Rs. 3000 for surrounding it from all the sides at Rs. 7.50 per metre. The difference between its length and breadth is :
A
`50 m`

B
`100 m`

C
`150 m`

D
`200 m`

Note: Let length = 5x and breadth = 3x in metres. Then, perimeter `= 2 (5x + 3x)` metres = 16x metres. But, perimeter `= Total cost/Rate/m` ` = (3000 xx 2/15) m` `= 400 m.` `:. 16x = 400 or x = 25.` :. Diff. in length & breadth `= (5x - 3x) = 2x = 50 m.`
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Question: In what ratio must rice at Rs. 9.30 per kg be mixed with rice at Rs. 10.80 per kg so that the mixture be worth Rs. 10 per kg?
A
7 : 8

B
8 : 7

C
31 : 36

D
36 : 31

Note: Not available
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Question: The length of a plot is four times its breadth. A play ground measuring 1200 sq.m. occupies one-third of the total area of the plot. What is the length of the plot ?
A
`20 m`

B
`30 m`

C
`60 m`

D
None

Note: Not available
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Question: In what ratio must wheat at Rs. 3.20 per kg be mixed with wheat at Rs. 2.90 per kg so that the mixture be worth Rs. 3.08 per kg?
A
4 : 3

B
3 3 : 4 3 : 4 3 : 4

C
2 : 3

D
3 : 2

Note: Not available
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Question: How many kilograms of sugar costing Rs. 9 per kg must be mixed with 27 kg of sugar costing Rs. 7 per kg so that there may be a gain of 10% by selling the mixture at Rs. 9.24 per kg ?
A
54 kg

B
63 kg

C
36 kg

D
42 kg

Note: Not available
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Question: The length of a rectangle is twice its breadth and one of its diagonals measure `10sqrt(5)` cm. The perimeter of the rectangle is :
A
`60 cm`

B
`50 cm`

C
`250 cm`

D
None

Note: Let breadth = x cm and length = 2x cm. Then, `x^2 + (2x)^2` `= (10sqrt(5)^2 or 5x^2` `= 500 or x^2` `= 100 or x = 10` :. perimeter` = 2 (2x + x) cm` `= 6x cm = 60 cm.`
1. Report

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Question: The cost of carpeting a room 18 m long with a carpet 75 cm wide at 45 paise per metre is Rs. 81. The breadth of the room is :

Question: A rectangular lawn 55 m by 35 m has two roads each 4 m wide running in the middle of it, one parallel to length and the other parallel to breadth. The cost of gravelling the roads at 75 paise per sq. metre is :

Question: A rectangular field has dimensions 25 m by 15 m. Two mutually perpendicular passages, 2 m wide have been left in the central part. In rest of the fields, grass has bee grown. The area under the grass is :

Question: The ratio between the length and breadth of a rectangular field is 5 : 4. If the breadth is 20 m less than the length, the perimeter of the field is :

Question: The length and breadth of a rectangular piece of land are in the ratio of 5 : 4 : 3. The owner spent Rs. 3000 for surrounding it from all the sides at Rs. 7.50 per metre. The difference between its length and breadth is :

Question: In what ratio must rice at Rs. 9.30 per kg be mixed with rice at Rs. 10.80 per kg so that the mixture be worth Rs. 10 per kg?

Question: The length of a plot is four times its breadth. A play ground measuring 1200 sq.m. occupies one-third of the total area of the plot. What is the length of the plot ?

Question: In what ratio must wheat at Rs. 3.20 per kg be mixed with wheat at Rs. 2.90 per kg so that the mixture be worth Rs. 3.08 per kg?

Question: How many kilograms of sugar costing Rs. 9 per kg must be mixed with 27 kg of sugar costing Rs. 7 per kg so that there may be a gain of 10% by selling the mixture at Rs. 9.24 per kg ?

Question: The length of a rectangle is twice its breadth and one of its diagonals measure `10sqrt(5)` cm. The perimeter of the rectangle is :