General Mathematics

Question: An amount of Rs. `735` was divided between `A, B` and `C`. If each of them had received Rs. `25` less, their shares would have been in the ratio of `1 : 3 : 2`. The money received by `C` was :
A
`Rs. 195`

B
`Rs. 200`

C
`Rs. 225`

D
`Rs. 245`

Note: Remainder `= Rs. (735 - (25 xx 3))` `= Rs. 660`. `:.` Money received by `C = Rs. [(660 xx 2/6) + 25]` `= Rs. 225`.
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Question: Half cubic metre of goldsheet is extended by hammering so as to cover an area of `1` hectare. The thickness of the sheet is :
A
`0.5 cm`

B
`0.05 cm`

C
`0.005 cm`

D
`.0005 cm`

Note: Volume of gold `= (1/2 xx 100 xx 100 xx 100) cu. cm`. Area of sheet `= 10000 sq. m` `= (10000 xx 100 xx 100) sq. cm.` :. Thickness of the sheet `= ((1 xx 100 xx 100 xx 100)/(2 xx 10000 xx 100 xx 100)) cm.` `= 0.005 cm.`
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Question: In a shower, `5` cm of rain falls. The valume of water that on `1.5` hectares of ground is :
A
`75 cu. m`

B
`750 cu. m`

C
`7500 cu. m`

D
`75000 cu. m`

Note: Area `= (1.5 xx 10000) sq. metres` `= 15000 sq. metres.` Depth`= 5/100 m = 1/20 m.` :. Volume` = (Area xx depth)` `= (15000 xx 1/20) cu. m` `= 750 cu. metres.`
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Question: A river `1.5 m`deep and `36` m wide is flowing at the rate of `3.5` km per hour. The amount of water that runs into the sea per minute ( in cubic metres) is :
A
`3150`

B
`31500`

C
`6300`

D
`63000`

Note: Length of water column flower in `1` min. `= ((3.5 xx 100)/(60)) m` `= 175/3 m.` :. Volume flower per minute `= (175/3 xx 36 xx 3/2) cu. m` `= 3150 cu. m.`
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Question: An amount of money is to be distributed among `P, Q` and `R` in the ration `3 : 5 : 7`. If `Q`'s share is Rs. `1500`, what is the difference between `p`'s and `R`'s shares ?
A
`Rs. 1200`

B
`Rs. 1500`

C
`Rs. 1600`

D
`Rs. 1900`

Note: Let `P = 3x, Q = 5x` and `R = 7x`. Then, `5x = 1500` `iff x = 300`. `:. P = 900, Q = 1500` and `R = 2100`. Hence, ` (R - P)` `= (2100 - 900)` `= 1200`
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Question: The area of the card board needed to make a box of size `24 cm xx 12 cm xx 5 cm` will be :
A
`1440 cm^2`

B
`468 cm^2`

C
`936 cm^2`

D
720 cm^2`

Note: Area of the cardboard `= 2(24 xx 12 + 12 xx 5 + 24 xx 5) cm^2` `= 936 cm^2.`
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Question: A sum of money is to the divided among `P, Q` and `R` in the ratio of `2 : 3 :5`. If the total share of `P` and `R` together is Rs `400` more than that of `Q` what is `R's` share in it ?
A
`Rs. 400`

B
`Rs. 500`

C
`Rs. 600`

D
`Rs. 750`

Note: Let `P = 2x, Q = 3x` and `R = 5x`. Now `P + R - Q = 400` `iff 2x + 5x - 3x = 400` `iff x = 100`. `:. R = 5x` `= 500`.
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Question: `X, Y` and `Z` share a sum of money in the ratio `7 : 8 : 16`. If `Z` receives `Rs. 27` more than `X`, then total money shared was :
A
`Rs. 48`

B
`Rs. 93`

C
`Rs. 279`

D
`Rs. 558`

Note: Let `X = 7x, Y = 8x & Z = 16x`. Then, total money `= 31x`. Now, `Z - X = 27` `iff 15x - 7x = 27` `iff x = 3`. `:.` Total money `= 31x` `= Rs. 93`.
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Question: A hall is `15` m long and `12` m broad. The sum of the areas of the floor and the ceiling is equal to the sum of areas of the areas of the four walls. The volume of the hall is :
A
`1200 m^3`

B
`1800 m^3`

C
`900 m^3`

D
`720 m^3`

Note: `2(15 + 12) xx h` `= 2(15 xx 12)` `or h = 180/27 m` `= 20/3 m.` :. Volume `= (15 xx 12 xx 20/3) m^3` `= 1200 m^3.`
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Question: An open box is made of wood `3` cm thick. Its external dimensions are `1.46 m``1.16 m` and `8.3 dm.` The cost of painting the inner surface of the box at `50` paise per `100` sq. cm is :
A
`Rs. 277`

B
`Rs. 138.50`

C
`Rs.415.50`

D
`Rs. 554`

Note: Internal length `= (146 - 6) cm = 140 cm,` Internal breadth `= (116 - 6) cm` `= 110 cm.` Internal depth `= (83 - 3) cm` `= 80 cm.` :. Area of inner surface `= [2 (1 + b) xx h] + 1b` `= [2 (140 + 110) xx 80 + 140 xx 110] sq. cm` `= 55400 sq. cm.` Cost of painting `= Rs. (1/2 xx 1/100 xx 55400)` `= Rs. 277`
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Question: An amount of Rs. `735` was divided between `A, B` and `C`. If each of them had received Rs. `25` less, their shares would have been in the ratio of `1 : 3 : 2`. The money received by `C` was :

Question: Half cubic metre of goldsheet is extended by hammering so as to cover an area of `1` hectare. The thickness of the sheet is :

Question: In a shower, `5` cm of rain falls. The valume of water that on `1.5` hectares of ground is :

Question: A river `1.5 m`deep and `36` m wide is flowing at the rate of `3.5` km per hour. The amount of water that runs into the sea per minute ( in cubic metres) is :

Question: An amount of money is to be distributed among `P, Q` and `R` in the ration `3 : 5 : 7`. If `Q`'s share is Rs. `1500`, what is the difference between `p`'s and `R`'s shares ?

Question: The area of the card board needed to make a box of size `24 cm xx 12 cm xx 5 cm` will be :

Question: A sum of money is to the divided among `P, Q` and `R` in the ratio of `2 : 3 :5`. If the total share of `P` and `R` together is Rs `400` more than that of `Q` what is `R's` share in it ?

Question: `X, Y` and `Z` share a sum of money in the ratio `7 : 8 : 16`. If `Z` receives `Rs. 27` more than `X`, then total money shared was :

Question: A hall is `15` m long and `12` m broad. The sum of the areas of the floor and the ceiling is equal to the sum of areas of the areas of the four walls. The volume of the hall is :

Question: An open box is made of wood `3` cm thick. Its external dimensions are `1.46 m``1.16 m` and `8.3 dm.` The cost of painting the inner surface of the box at `50` paise per `100` sq. cm is :