Ratio & Proportion, General Mathematics

Question: An amount of Rs. `2430` is divided among `A, B` and `C` such that if their shares be reduced by Rs. `5` Rs. `10` and Rs. `15` respectively, the remainders shall be in the ratio`3 : 4 : 5`. The share of `B` is :
A
`Rs. 605`

B
`Rs. 790`

C
`Rs. 800`

D
`Rs. 810`

Note: Remainder `= Rs. [2430 - (5 + 10 + 15)]` `= Rs. 2400`. `:. B's ` share `= Rs.[(2400 xx 4/(12)) + 10]` `= Rs. 810`.
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Question: An amount of Rs. `735` was divided between `A, B` and `C`. If each of them had received Rs. `25` less, their shares would have been in the ratio of `1 : 3 : 2`. The money received by `C` was :
A
`Rs. 195`

B
`Rs. 200`

C
`Rs. 225`

D
`Rs. 245`

Note: Remainder `= Rs. (735 - (25 xx 3))` `= Rs. 660`. `:.` Money received by `C = Rs. [(660 xx 2/6) + 25]` `= Rs. 225`.
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Question: An amount of money is to be distributed among `P, Q` and `R` in the ration `3 : 5 : 7`. If `Q`'s share is Rs. `1500`, what is the difference between `p`'s and `R`'s shares ?
A
`Rs. 1200`

B
`Rs. 1500`

C
`Rs. 1600`

D
`Rs. 1900`

Note: Let `P = 3x, Q = 5x` and `R = 7x`. Then, `5x = 1500` `iff x = 300`. `:. P = 900, Q = 1500` and `R = 2100`. Hence, ` (R - P)` `= (2100 - 900)` `= 1200`
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Question: A sum of money is to the divided among `P, Q` and `R` in the ratio of `2 : 3 :5`. If the total share of `P` and `R` together is Rs `400` more than that of `Q` what is `R's` share in it ?
A
`Rs. 400`

B
`Rs. 500`

C
`Rs. 600`

D
`Rs. 750`

Note: Let `P = 2x, Q = 3x` and `R = 5x`. Now `P + R - Q = 400` `iff 2x + 5x - 3x = 400` `iff x = 100`. `:. R = 5x` `= 500`.
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Question: `X, Y` and `Z` share a sum of money in the ratio `7 : 8 : 16`. If `Z` receives `Rs. 27` more than `X`, then total money shared was :
A
`Rs. 48`

B
`Rs. 93`

C
`Rs. 279`

D
`Rs. 558`

Note: Let `X = 7x, Y = 8x & Z = 16x`. Then, total money `= 31x`. Now, `Z - X = 27` `iff 15x - 7x = 27` `iff x = 3`. `:.` Total money `= 31x` `= Rs. 93`.
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Question: A profit of Rs. `30000` is to distributed among `A, B, C` in the proportion `3 : 5 : 7`. What will be the difference between `B's` and `C's` shares ?
A
`Rs. 2000`

B
`Rs. 4000`

C
`Rs. 10000`

D
`Rs. 14000`

Note: `B's` share `= Rs. (30000 xx 5/(15))` `= Rs. 10000`. `C's` share `= Rs. (30000 xx 7/(15))` `= Rs. 14000`. `:.` Difference in `B's & C's ` shares `= Rs. 4000`.
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Question: Rs. `407` are to be divided among `A, B` and `C` so that their shares are in the ratio of `1/4 : 1/5 : 1/6`. The respective shares of `A, B, C` are :
A
`Rs. 165, Rs. 132, Rs. 110`

B
`Rs. 165, Rs. 110, Rs. 132`

C
`Rs. 132, Rs. 110, Rs. 165`

D
`Rs. 110, Rs. 132, Rs. 165`

Note: `A : B : C = 1/4 : 1/5 : 1/6` `= 15 : 12 : 10` `A's` share `= Rs. (407 xx (15)/(37))` `= Rs. 165`, `B's` share `= Rs. (407 xx (12)/(37))` `= Rs. 132`, `C.s` share `= Rs. [407 - (165 + 132)]` `= Rs. 110`
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Question: If Rs `1066` are divided among `A, B, C` and `D` such that `A : B = 3 : 4, B : C = 5 : 6`and `C : D = 7 : 5`, who will get the maximum ?
A
`B`

B
`A`

C
`C`

D
`D`

Note: `A : B = 3 : 4`, `B : C = 5 : 6` `= 5 xx 4/5 : 6 xx 4/5` `= 4 : (24)/5`. `:. A : B : C = 4 : (24)/5` `= 15 : 20 : 24 & C : D = 7 : 5` or `A : B : C = 15 : 2o : 24 & C : D = (24)/7 xx 7 : (24)/7 xx 5` or` A : B : C = 15 : 2o : 24 & C : D = 24 : (120)/7`. `:. A : B : C : D = 15 : 20 : 24 : (120)/7` `= 105 : 140 : 168 : 120` Clearly, `C` will get the maximum amount.
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Question: A certain amount was divided between Salim and Rahim in the ratio of `4 : 3`. If Rahim's share was Rs. `2400`, the total amount was :
A
`Rs. 5600`

B
`Rs. 3200`

C
`Rs. 9600`

D
`Rs. 16800`

Note: Let `S =4x` and `R = 3x`. Total amount `= 7x` Then, `3x = 2400` `iff x = 800`. `:.` Total amount `= 7x` `= Rs. 5600`
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Question: The ratio of the ages of mother and son is `7 : 3`. If the sum of their ages is `60` years, what is the difference in their ages ?
A
`42` years

B
`24` years

C
`18` years

D
`4` years

Note: Mother's age `= (60 xx 7/(10))` `= 42` years. Son's age `=(60 - 42)`years `= 18`years. Difference of their ages `= (42 - 18)`years `= 24` years.
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Question: An amount of Rs. `2430` is divided among `A, B` and `C` such that if their shares be reduced by Rs. `5` Rs. `10` and Rs. `15` respectively, the remainders shall be in the ratio`3 : 4 : 5`. The share of `B` is :

Question: An amount of Rs. `735` was divided between `A, B` and `C`. If each of them had received Rs. `25` less, their shares would have been in the ratio of `1 : 3 : 2`. The money received by `C` was :

Question: An amount of money is to be distributed among `P, Q` and `R` in the ration `3 : 5 : 7`. If `Q`'s share is Rs. `1500`, what is the difference between `p`'s and `R`'s shares ?

Question: A sum of money is to the divided among `P, Q` and `R` in the ratio of `2 : 3 :5`. If the total share of `P` and `R` together is Rs `400` more than that of `Q` what is `R's` share in it ?

Question: `X, Y` and `Z` share a sum of money in the ratio `7 : 8 : 16`. If `Z` receives `Rs. 27` more than `X`, then total money shared was :

Question: A profit of Rs. `30000` is to distributed among `A, B, C` in the proportion `3 : 5 : 7`. What will be the difference between `B's` and `C's` shares ?

Question: Rs. `407` are to be divided among `A, B` and `C` so that their shares are in the ratio of `1/4 : 1/5 : 1/6`. The respective shares of `A, B, C` are :

Question: If Rs `1066` are divided among `A, B, C` and `D` such that `A : B = 3 : 4, B : C = 5 : 6`and `C : D = 7 : 5`, who will get the maximum ?

Question: A certain amount was divided between Salim and Rahim in the ratio of `4 : 3`. If Rahim's share was Rs. `2400`, the total amount was :

Question: The ratio of the ages of mother and son is `7 : 3`. If the sum of their ages is `60` years, what is the difference in their ages ?