General Mathematics

Question: `20` litres of a mixture contains milk and water in the ratio `5 : 3`. If `4` litres of this mixture are replaced by `4` litres of milk, the fatio of milk to water in the new mixture will become :
A
`2 : 1`

B
`7 : 3`

C
`8 : 3`

D
`4 : 3`

Note: Milk in `16` litres `= (16 xx 5/8)litres `= 10` litres. Water in `16` litres `= (16 - 10)litres `= 6`litres. `:.` Ratio of milk in new mixture `=(10 + 4) = 14`litres. Milk in new mixture `= (10 + 4) = 14` litres. `:.` Ratio of milk and water in new mix. `= 14 : 6 = 7 : 3`.
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Question: `A` and `B` are two alloys of gold and copper prepared by mixing metals in the ratio `7 : 2` and `7 : 11` respectively. If equal quantities of the alloys are melted to form a third alloy `C`, the ratio of gold and copper in `C` will be :
A
`5 : 9`

B
`5 : 7`

C
`7 : 5`

D
`9 : 5`

Note: Gold in `C = (7/9 + 7/(18)) = 7/6.` Copper in `C = (2/9 + (11)/(18)) = 5/6.` Gold : Copper `= 7/6 : 5/6 = 7 : 5.`
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Question: A mixture contains milk and water in the ratio `5 : 1`. On adding `5` litres of water, the ratio of milk to water becomes `5 : 2`. The quantity of milk in the original mixture is :
A
`16` litres

B
`25` litres

C
`22.75` litres

D
`32.5` litres

Note: Let milk `= 5x` and water `= x`. Then, `(5x)/(x + 5) = 5/2` or `10x = 5x + 25` or `x = 5`. `:.` Quantity of milk in given mix. `= 25` litres.
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Question: If `x%` of y is the same as`4/5` of `80`, then the value of `xy` is :
A
`320`

B
`400`

C
`640`

D
None

Note: `x/(100) xx y` `= 4/5 xx 80 ⇒ xy` `= 64 xx 100` `= 6400`
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Question: Subtracting `6%` of x from x is equivalent to multiplying x by how much ?
A
`.94`

B
`9.4`

C
`.094`

D
`94`

Note: Let `x - 6% of x = xz.` Then,`94% of x = xz` `or 94/(100) x xx 1/x = z` `or z = .94`
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Question: Two equal glasses are respectively `1/3` and `1/4` full of milk. They are then filled with water and the contents mixed in a tumbler. The ratio of milk and water in the tumbler is :
A
`7 : 5`

B
`7 : 17`

C
`9 : 21`

D
`11 : 23`

Note: First glass contains Milk `= 1/3`, Water `= 2/3`. Second glass contains Milk `= 1/4`,Water `= 3/4`. New tumbler contains : Milk `= (1/3 + 1/4) = 7/(12)`, Water `= (2/3 + 3/4) = (17)/(12)`. `:.` Ratio of Milk & Water `= 7/(12) : (17)/(12)`.
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Question: Three bottles are filled with a mixture of milk and water in the ratio `4 : 3, 5 : 4` and `7 : 6` respectively. If the contents of three bottles are poured into a single vesse, then the ratio of milk to water in the new vessel is :
A
`(4/3 + 5/4 + 7/6 : 3/4 + 4/5 + 6/7)`

B
`(4/7 + 5/9 + 7/(13) : 3/7 + 4/9 + 6/(13))`

C
`(4/3 + 5/4 + 7/6 : 1 + 1 +1)`

D
`(1 + 1 + 1 : 3/4 + 4/5 + 6/7)`

Note: In new vessel, we have : Milk `= (4/7 + 5/9 + 7/(13))` Water `=(3/7 + 4/9 + 6/(13))` `:.` Milk : Water `= (4/7 + 5/9 + 7/(13)) : (3/7 + 4/9 + 6/(13))`.
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Question: If` 8% of x = 4%` of y, then` 20%` of x is :
A
`10%` of y

B
`16%` of y

C
`80%` of y`

D
None of these

Note: `8/(100) x` ` = 4/(100) y ⇒ x` `= (4/(100) y xx 100/8)` `= 1/(2) y`
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Question: `(x% of y + y% of x) = ?`
A
`x%` of y

B
`y%` of x

C
`2%` of xy

D
`xy% of 3`

Note: `x/(100) y + y/(100) x` `= (2xy)/(100)` `= 2% of xy.`
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Question: The price of `357` mangoes is `Rs. 1517.25`. What will be the approximate price of `49` dozens of such mangoes ?
A
`Rs. 3000`

B
`Rs. 3500`

C
`Rs. 4000`

D
`Rs. 2500`

Note: More mangoes, more cost (Direct) `357 : 49 xx 12 :: 1517.25 : x` or `375 xx x = 49 xx 12 xx 1517.25`. `:. x = ((49 xx 12 xx 1517.25)/(357))` `= 2499`. `:.` Approximate cost `= Rs. 2500`.
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Question: `20` litres of a mixture contains milk and water in the ratio `5 : 3`. If `4` litres of this mixture are replaced by `4` litres of milk, the fatio of milk to water in the new mixture will become :

Question: `A` and `B` are two alloys of gold and copper prepared by mixing metals in the ratio `7 : 2` and `7 : 11` respectively. If equal quantities of the alloys are melted to form a third alloy `C`, the ratio of gold and copper in `C` will be :

Question: A mixture contains milk and water in the ratio `5 : 1`. On adding `5` litres of water, the ratio of milk to water becomes `5 : 2`. The quantity of milk in the original mixture is :

Question: If `x%` of y is the same as`4/5` of `80`, then the value of `xy` is :

Question: Subtracting `6%` of x from x is equivalent to multiplying x by how much ?

Question: Two equal glasses are respectively `1/3` and `1/4` full of milk. They are then filled with water and the contents mixed in a tumbler. The ratio of milk and water in the tumbler is :

Question: Three bottles are filled with a mixture of milk and water in the ratio `4 : 3, 5 : 4` and `7 : 6` respectively. If the contents of three bottles are poured into a single vesse, then the ratio of milk to water in the new vessel is :

Question: If` 8% of x = 4%` of y, then` 20%` of x is :

Question: `(x% of y + y% of x) = ?`

Question: The price of `357` mangoes is `Rs. 1517.25`. What will be the approximate price of `49` dozens of such mangoes ?