Simplification, General Mathematics

Question: If `x/y = 4/5`, the value of `(5/8 + (y - x)/(y + x))`is
A
`49/72`

B
`53/72`

C
`23/72`

D
None of these

Note: `(5/8 + (y - x)/(y + x))` `= (5/8 + (1 - x/y)/(1 + x/y))` `= (5/8 + (1 - 4/5)/(1 + 4/5))` `= 5/8 + ((1∕5))/((9∕5))` `= (5/8 + 1/5 xx 5/9)` `= 5/8 + 1/9)` `= 3/72`
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Question: If `a/2b = 3/2`, then the value of `(2a + b)/(a - 2b)` equals :
A
`1/7`

B
`7`

C
`7.1`

D
None of these

Note: Not available
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Question: If`a/b = 1/5`, then (5a + 2b)/(5a - 2b)` is equal to :
A
`3`

B
`- 3`

C
`- 5`

D
`-1`

Note: `(5a + 2b)/(5a - 2b)` `= 5 (a/b) + 2/5 (a/b) - 2` `= (5 xx 1/5 +2)/(5 xx 1/5 - 2)` `= 3/(1 -2)` `= -3`
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Question: If`a/3 = b/4 = c/7`, the value of (a + b + c)/c `is :
A
`7`

B
`2`

C
`1/2`

D
`1/7`

Note: Let,`a/3 = b/4 = c/7 = k`. Then,`a = 3k, b = 4k & c = 7k`. :.`(a + b + c)/c` `= (3k + 4k + 7k)/7k` `= (14k)/(7k)` `= 2`.
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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 ?
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: If `x/y = 4/5`, the value of `(5/8 + (y - x)/(y + x))`is

Question: If `a/2b = 3/2`, then the value of `(2a + b)/(a - 2b)` equals :

Question: If`a/b = 1/5`, then (5a + 2b)/(5a - 2b)` is equal to :

Question: If`a/3 = b/4 = c/7`, the value of (a + b + c)/c `is :

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 ?