General Mathematics

Question: A tin of oil was `4/3`full.When `6`bottles of oil were poured onto it,it was `3/4` full.How many bottles of oil can the tin contain ?
A
`10`

B
`20`

C
`30`

D
`40`

Note: `4/5 - 2`bottles = `3/4` or `2`bottles `= (4/3 - 3/4) = 1/20` :.`40 bottles will fill the can.
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Question: If we multiply a fraction by otself and divide the product by its reciprocal the fraction thus obtained is `18 26/27`.The original fraction is :
A
`8/27`

B
`2 2/3`

C
`1 1/3`

D
None of these

Note: Let fraction be,`a/b`.Then, `(a/b xx a/b) ÷ b/a` `= 512/27` or ` a/b xx a/b xx a/b` `= 512/27`. `:. (a/b)^3 = (8/3)^3` or ` a/b = 8/3` or` a/b = 2 2/3`.
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Question: A bpy multiplied `423` by a number and obtained `65589` as his answer.If both the fives in the answer are wrong and all other figures are correct, the correct answer is :
A
`62389`

B
`61189`

C
`62189`

D
`60489`

Note: Among the given choices only `60489` is a multiply of `423`.
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Question: In a family, the father took `1/4` of the cake and he had 3 times as much as others had. The total number of family members is :
A
`3`

B
`7`

C
`10`

D
`12`

Note: Let there be `(x + 1)`members. Father 's share `= 1/4`,share of each other member `= 3/(4x)` :.` 3 (3/(4x)) = 1/4` or ` 4x = 36` or ` x 9`. :. The total number of family members `= 10`.
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Question: The charges of hired car are Rs`4` per km for the first `60` km ,Rs `5` per km for the next `60` km and Rs `8` for every `5` km for further journey .If the balance amount left over with subhash is `1/4`of what he paid towards the charges of the hired car for travelling `320`km ,how much money did he have initialy with him ?
A
`Rs 1075`

B
`Rs 1255`

C
`Rs 1540`

D
None of these

Note: Hire charges `= Rs(60 xx 4 + 60 xx 5 + 8/5 xx 200)` `= Rs.860`. Now surpose Subhhash had Rs .x with him intially. Then ,`x - 860 = 1/4 xx 860` or x = 1075`.
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Question: The rent of a guest house was Rs `50`per day for first three days ,Rs `100`per day for next `5`days and Rs `300`per day for other days .The registration fee in the begining is Rs`50`.If one has to pay Rs `1300`,for how many days he availed of this facility ?
A
`7`

B
`8`

C
`9`

D
`10`

Note: `(50 + 50 xx 3 + 100 xx 5 + x xx 300)= 1300` or `300x = 600` or` x = 2`. :. Total number of days `= (3 + 5 + 2) days = 10 days `.
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Question: In a certain office,`1/3` of the workers are women,`1/2`of the women are married and `1/3`of the married women have children.If`3/4`of the men are married and `3/4`of the married and `2/3` of the married men have children,what part of workers are without children ?
A
`5/18`

B
`4/9`

C
`11/18`

D
`17/36`

Note: Let the total number of workers be x. Then,`w =x/3`and `M = (2x)/3` Women having children `= 1/3 of 1/2 of 1/3 x = x/18` Men having children `= 2/3 of 3/4 of (2x)/3 = x/3` Workers having children `= (x/18 + x/3) = (7x)/18` Workers having no children `= (x - (7x)/18) = (11x)/18` `= 11/18` of all workers.
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Question: A train starts full of passengers and takes `280` more .At the seceond station,it drops one half of the new total anf takes `12`more .On arriving at the third station ,it is found to have `248`passengers .The number of passsengers in the begining was :
A
`156`

B
`288`

C
`564`

D
`608`

Note: Let the number of passengers in the begining be x, After 1st station ,passengers `= (x - x/3) + 280` `= ((2x)/3 + 280)` After 2nd starion ,passengers `= ((2x)/3 +280) - 1/2 ((2x)/3 + 280) + 12` `:. 1/2((2x)/3 + 280) + 12= 248` `or (2x)/3 + 280` `= 2 xx 236` `or (2x)/3 = 192` `:. x = (192 xx 3/2) = 288`.
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Question: One test tube contains some acid and another test tube contains an equal quantity o f water. To prepare a soluation ,`20`grams of the acid is poured into the second test tube .Then two thirds of the so formed solition is poured from the second tube into the first.If the fluid in the first test tube is four times that in the second ,what quantity of water was taken intially,
A
`40 grams`

B
`60 grams`

C
`80 grams`

D
`100 grams`

Note: Suppose each tube contains x gms initially. `4[1/3(x + 20)]` `= x + 2/3 (x + 20)` or `2/3 (x + 20) = x` or` x/3 = 40/3` `:. x = 40`
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Question: Four a group of boys and girls `15` girls leave.There are then left `2` boys for each girl.After this, `45` boys leave. There are then `5`girls for each boy.The number of girls in the begining was:
A
`40`

B
`43`

C
`29`

D
`50`

Note: Let at present there be x boys. Then,the number of girls at present `= 5x`. Before the boys have left: Number of boys`= x + 45` and number of girls`= 5x` :.`x + 45 ` `= 2 (5x) ⇒ 9x` `= 45 ⇒ x = 5`. Hence,the number of girls in the beginig `= 5x + 15` `= 25 + 15` `= 40`
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Question: A tin of oil was `4/3`full.When `6`bottles of oil were poured onto it,it was `3/4` full.How many bottles of oil can the tin contain ?

Question: If we multiply a fraction by otself and divide the product by its reciprocal the fraction thus obtained is `18 26/27`.The original fraction is :

Question: A bpy multiplied `423` by a number and obtained `65589` as his answer.If both the fives in the answer are wrong and all other figures are correct, the correct answer is :

Question: In a family, the father took `1/4` of the cake and he had 3 times as much as others had. The total number of family members is :

Question: The rent of a guest house was Rs `50`per day for first three days ,Rs `100`per day for next `5`days and Rs `300`per day for other days .The registration fee in the begining is Rs`50`.If one has to pay Rs `1300`,for how many days he availed of this facility ?

Question: In a certain office,`1/3` of the workers are women,`1/2`of the women are married and `1/3`of the married women have children.If`3/4`of the men are married and `3/4`of the married and `2/3` of the married men have children,what part of workers are without children ?

Question: A train starts full of passengers and takes `280` more .At the seceond station,it drops one half of the new total anf takes `12`more .On arriving at the third station ,it is found to have `248`passengers .The number of passsengers in the begining was :

Question: Four a group of boys and girls `15` girls leave.There are then left `2` boys for each girl.After this, `45` boys leave. There are then `5`girls for each boy.The number of girls in the begining was: