Ratio & Proportion, General Mathematics

Question: The speeds of the ages of three cars are in the ratio `5 : 4 : 6`. The ratio between the times taken by them to travel the same distance is :
A
`5 : 4 : 6`

B
`6 : 4 : 5`

C
`10 : 12 : 15`

D
`12 : 15 : 10`

Note: Ratio of times taken `= 1/5 : 1/4 : 1/6` `= 12 : 15 : 10`
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Question: The sides of a triangle are in the ratio `1/2 : 1/3 : 1/4` and its perimeter is `104 cm`. The length of longest side is :
A
`52 cm`

B
`48 cm`

C
`32 cm`

D
`26 cm`

Note: Ratio of sides `= 1/2 : 1/3 : 1/4` `= 6 : 4 : 3`. Largest side `= ( 104 xx 6/(13)) cm` `= 48 cm`.
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Question: In a college, the ratio of the number of boys to girls is `8 : 5`. If there are `160` girls, the total number of students in the college is :
A
`100`

B
`250`

C
`260`

D
`416`

Note: Let the number of boys and girls be `8x` and `5x`. Then , total number of students `= 13x`. Now, `5x = 160` `iff x = 32`. `:.` Total number of students `= 13x ` `= 13 xx 32` `= 416`.
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Question: The prices of a scooter and T.V. are in the ratio of `5 : 4`. If the scooter costs Rs. `4000` more than the T.V. set , the price of a T.V. set (in rupees) is :
A
`12000`

B
`14000`

C
`16000`

D
`20000`

Note: Let the costs of scooter & T.V. be `5x` and `4x`. Then, ` 5x - 4x = 4000` `iff x = 4000`. `:.` Cost of a T.V. `= 4x` `= Rs. 16000`.
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Question: Pencils, Pens and Exercise books in a shop are in the ratio of `10 : 2 : 3`. If there are `120`pencils, the mumber of exercise books in the shop is :
A
`36`

B
`48`

C
`72`

D
`400`

Note: Let Pencils `= 10x`, Pens `= 2x` & Exercise books `= 3x` Now, `10x = 120` `iff x = 12`. `:.` Number of exercise books `= 3x` `= 36 `.
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Question: In a factory, the ratio of male workers to female workers was `5 : 3`. If the number of female workers workers was less by `40` what was the total number of workers in the factory?
A
`100`

B
`160`

C
`200`

D
`500`

Note: Let males `= 5x` and females `= 3x`. Then, total `= 8x`. Now, `5x - 3x = 40` `iff x = 20`. `:.` Total number of workers in the factory `= 8x` `= 160`.
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Question: An alloy is to contain copper and zinc in the ratio `9 : 4`. The zinc required (in kg) to be melted with `24` kg of copper, is ?
A
`10 2/3`

B
`10 1/3`

C
`9 2/3`

D
`9`

Note: `9 : 4 :: 24 : x` `iff 9x = 4 xx 24` `iff x = (4 xx 24)/9` `= 10 2/3` kg.
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Question: The ratio of income of `A` to that of `B` is `5 : 4` and the expenditure of `A` to that of `B` is `3 : 2`. If at the end of the year, each saves Rs. `800`, the income of `A` is :
A
Rs. `1600`

B
Rs. `1800`

C
Rs. `2000`

D
Rs. `2200`

Note: Let the income of `A` and `B` be ` 5x & 4x` and the expenditures of `A`and`B` be`3y` and `2y`. Then, `5x - 3y = 800` and `4x - 2y = 800`. On solving we get `: x = 400`. `:. A's` income `= 5x` `= Rs. 2000`.
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Question: A dog takes `3` leaps for every `5` leaps of a hare. If one leap of the dog is equal to `3` leaps of the hare, the ratio of the speed of the dog to that of the hare is :
A
`8 : 5`

B
`9 : 5`

C
`8 : 7`

D
`9 : 7`

Note: Dog : Hare `= (3 xx 3)` leaps of hare `: 5` leaps of hare `= 9 : 5`.
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Question: `60`kg of an alloy `A` is mixed with `100` kg of alloy `B`. If alloy `A` has lead and tin in the ratio `3 : 2` and alloy `B` has tin and copper in the ratio `1 : 4`, then the amount of tin in the new alloy is :
A
`36`kg

B
`44`kg

C
`53`kg

D
`80`kg

Note: Tin in `60`kg. of `A = ( 60 xx 2/5)` `= 24` kg. Tin in `100`kg of `B = ( 100 xx 1/5)` `= 20` kg. `:.`Amount of tin in new alloy `= ( 24 + 20 )` kg `= 44` kg.
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Question: The speeds of the ages of three cars are in the ratio `5 : 4 : 6`. The ratio between the times taken by them to travel the same distance is :

Question: The sides of a triangle are in the ratio `1/2 : 1/3 : 1/4` and its perimeter is `104 cm`. The length of longest side is :

Question: In a college, the ratio of the number of boys to girls is `8 : 5`. If there are `160` girls, the total number of students in the college is :

Question: The prices of a scooter and T.V. are in the ratio of `5 : 4`. If the scooter costs Rs. `4000` more than the T.V. set , the price of a T.V. set (in rupees) is :

Question: Pencils, Pens and Exercise books in a shop are in the ratio of `10 : 2 : 3`. If there are `120`pencils, the mumber of exercise books in the shop is :

Question: In a factory, the ratio of male workers to female workers was `5 : 3`. If the number of female workers workers was less by `40` what was the total number of workers in the factory?

Question: An alloy is to contain copper and zinc in the ratio `9 : 4`. The zinc required (in kg) to be melted with `24` kg of copper, is ?

Question: The ratio of income of `A` to that of `B` is `5 : 4` and the expenditure of `A` to that of `B` is `3 : 2`. If at the end of the year, each saves Rs. `800`, the income of `A` is :

Question: A dog takes `3` leaps for every `5` leaps of a hare. If one leap of the dog is equal to `3` leaps of the hare, the ratio of the speed of the dog to that of the hare is :

Question: `60`kg of an alloy `A` is mixed with `100` kg of alloy `B`. If alloy `A` has lead and tin in the ratio `3 : 2` and alloy `B` has tin and copper in the ratio `1 : 4`, then the amount of tin in the new alloy is :