General Mathematics

Question: The surface area of a cube is `1734` sq. cms. Its volume is :
A
`2197 cu. cm`

B
`4913 cu. cm`

C
`2744 cu. cm`

D
`4096 cu. cm`

Note: `6a^2 = 1734 ⇒ a^2 = 289` `or a = 17 cm`. :. Volume`= (17 xx 17 xx 17) cu. cm` `= 4913 cu. cm`.
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Question: The surface area of a cube is `600 cm^2`. The length of its diagonal is :
A
`10/√3 cm`

B
`10/√2 cm`

C
`10√3 cm`

D
`10√2 cm`

Note: `6a^2 = 600 ⇒ a^2 = 100` `or a = 10 cm`. `:. Diagonal = √3 a = 10√3 cm`.
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Question: The volume of a cube is `2744 cu. cm.` Its surface area is :
A
`196 cm^2`

B
`1176 cm^2`

C
`784 cm^2`

D
`588 cm^2`

Note: `a^3 = 2744` `= (2 xx 2 xx 2 xx 7 xx 7 xx 7) ⇒ a` `= 14 cm.` :. Surface Area `= 6a^2 = (6 xx 14 xx 14) cm^2` `= 1176 cm^2`.
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Question: The sum of the length, breadth and depth of a cuboid is `19` cm and its diagonal is `5√5 cm`. Its surface area is :
A
`361 cm^2`

B
`125 cm^2`

C
`236 cm^2`

D
`486 cm^2`

Note: `(1 + b + h) ` `= 19 & √1^2 + b^2 + h^2` `= 5√5 and so (1^2 + b^2 + h^2)` `= 125` Now`(1 + b + h)^2 = 19^2` `⇒ (1^2 + b^2 + h^2) + 2 (1b + bh + 1h) = 361` `⇒ 2 (1b + bh + 1h)` `= (361 - 125)` `= 236`. :. Surface area `= 236 cm^2.`
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Question: The area of the base of a rectangular tank is `6500 cm^2` and the volume of water contained in its `2.6` cubic metres. The depth of water in the tank is :
A
`3.5 m`

B
`4 m`

C
`5 m`

D
`6 m`

Note: Volume`= (2.6 xx 100 xx 100 xx 100) cubic cm`. Depth` = Volume/Area of the base` `= ((2.6 xx 100 xx 100 xx 100)/(6500)) cm` `= 4 m`.
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Question: The salaries of `A, B,` and `C` are in the ratio of `1 : 2 : 3`. The salary of `B` and `C` together is Rs. `6000`. By what percent is the salary of `C` more than that of `A` ?
A
`100%`

B
`200%`

C
`300%`

D
`600%`

Note: Let the salaries of `A, B, C` be `x, 2x` and `3x` respectively. Then, `2x + 3x = 6000` `iff x = 1200`. `:. A's`salary `= Rs. 1200, B's ` salary `= Rs. 2400`, and `C's` salary `= Rs. 3600`. `:.` Excess of `C's` salary over `A's = ((2400)/(1200) xx 100)%` `= 200%`
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Question: The average age of three boys is `25` years and their ages are in the proportion `3 : 5 : 7`. The age of the youngest boy is :
A
`21` years

B
`18` years

C
`15` years

D
`9` years

Note: Total age of 3 boys `= (25 xx 3)`years `= 75` years. `:.` Age of the youngest `= (75 xx 3/(15))` `= 15` years.
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Question: Given that `1` cu. cm of marble weighs `25` gms, the weight of a marble block `28` cm in width and`5` cm thick is `112` kg. The length of the block is :
A
`36 cm`

B
`40 cm`

C
`32 cm`

D
`26.5 cm`

Note: Let length = x cm. Then` x xx 28 xx 5 xx 25/1000` `= 112` `:. x = (112 xx 1000/25 xx 1/28 xx 1/5) cm` `= 32 cm.` `:. Length of block = 32 cm`.
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Question: An amount of Rs. `2430` is divided among `A, B` and `C` such that if their shares be reduced by Rs. `5` Rs. `10` and Rs. `15` respectively, the remainders shall be in the ratio`3 : 4 : 5`. The share of `B` is :
A
`Rs. 605`

B
`Rs. 790`

C
`Rs. 800`

D
`Rs. 810`

Note: Remainder `= Rs. [2430 - (5 + 10 + 15)]` `= Rs. 2400`. `:. B's ` share `= Rs.[(2400 xx 4/(12)) + 10]` `= Rs. 810`.
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Question: The volume of a wall,`5` times as high as it is broad and `8` times as long as it is high, is `12.8` cu. mertres. The breadth of the wall is :
A
`30 m`

B
`40 m`

C
`22.5 m`

D
`25 m`

Note: Let, breadth = x mertres. Then, Heigth` = 5x` mertres and length `= 40 x` mertres. `:. x xx 5x xx 40x` `= 12.8` `or x^3 = 12.8/200` `= 128/2000` `= 64/1000.` `:. x 4/10 m` `= (4/10 xx 100) cm` `= 40 cm.`
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Question: The surface area of a cube is `1734` sq. cms. Its volume is :

Question: The surface area of a cube is `600 cm^2`. The length of its diagonal is :

Question: The volume of a cube is `2744 cu. cm.` Its surface area is :

Question: The sum of the length, breadth and depth of a cuboid is `19` cm and its diagonal is `5√5 cm`. Its surface area is :

Question: The area of the base of a rectangular tank is `6500 cm^2` and the volume of water contained in its `2.6` cubic metres. The depth of water in the tank is :

Question: The salaries of `A, B,` and `C` are in the ratio of `1 : 2 : 3`. The salary of `B` and `C` together is Rs. `6000`. By what percent is the salary of `C` more than that of `A` ?

Question: The average age of three boys is `25` years and their ages are in the proportion `3 : 5 : 7`. The age of the youngest boy is :

Question: Given that `1` cu. cm of marble weighs `25` gms, the weight of a marble block `28` cm in width and`5` cm thick is `112` kg. The length of the block is :

Question: An amount of Rs. `2430` is divided among `A, B` and `C` such that if their shares be reduced by Rs. `5` Rs. `10` and Rs. `15` respectively, the remainders shall be in the ratio`3 : 4 : 5`. The share of `B` is :

Question: The volume of a wall,`5` times as high as it is broad and `8` times as long as it is high, is `12.8` cu. mertres. The breadth of the wall is :