Ratio & Proportion, General Mathematics

Question: `85` kg of a mixture contains milk and water in the ratio `27 : 7`. How much more water is to be added to get a new mixture containing milk and water in the ratio `3 : 1` ?
A
`5` kg

B
`6.5` kg

C
`7.25` kg

D
`8` kg

Note: Milk in `85` kg `= (85 xx (27)/(34))` kg `= (135)/2` kg. Water in `85` kg `= (85 xx (135)/2)` kg `= (35)/2` kg. Let `x` kg of water be added. `(Milk)/(Water) = 3/1` `iff ((135)/2)/((35)/2 + x) = 3/1` or `(135)/(35 + 2x) = 3/1` or `6x + 105 = 135` or `x = 5` kg.
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Question: `15` litres of a mixture contains `20%` alcohol and the rest water. If `3` litres of water be mixed in it, the percentage of alcohol in the new mixture will be :
A
`15`

B
`16 2/3`

C
`17`

D
`18 1/2`

Note: Alcohol in `15` litres `= ((20)/(100) xx 15)` litres `= 3` litres. Percentage of alcohol in new mix. `= (3/(15 + 3) xx 100)%` `= 16 2/3 %`
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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 :
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: 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: `85` kg of a mixture contains milk and water in the ratio `27 : 7`. How much more water is to be added to get a new mixture containing milk and water in the ratio `3 : 1` ?

Question: `15` litres of a mixture contains `20%` alcohol and the rest water. If `3` litres of water be mixed in it, the percentage of alcohol in the new mixture will be :

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: 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 :