Ratio & Proportion, General Mathematics

Question: `Rs. 730` were divided among `A, B, C` in such a way that if `A` gets `Rs. 3`, then `B` gets `Rs. 4` and if `B` gets `Rs. 3.50` then `C` gets `Rs. 3`. The share of `B` exceeds that of `C` by :
A
`Rs. 30`

B
`Rs. 40`

C
`Rs. 70`

D
`Rs. 210`

Note: `A : B = 3 : 4` and `B : C = 7/2 : 3` `= 8/7 xx 7/2 : 8/7 xx 3` `= 4 : (24)/7` `A : B : C = 3 : 4 : (24)/7` `= 21 : 28 : 24`. `B's` share `= Rs. (730 xx (28)/(73))` `= Rs. 280`. `C's` share `= Rs. (730 xx (24)/(73))` `= Rs. 240`. `:.` Difference of their shares `= Rs. 40`.
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Question: `Rs. 53`are divided among three persons `A, B, C` in such a way that `A`gets `Rs 7` more than what `B` gets and `B` gets `Rs. 8` more than what `C`gets. The ratio of their shares is :
A
`16 : 9 : 18`

B
`25 : 18 : 10`

C
`18 : 25 : 10`

D
`15 : 8 : 30`

Note: Let `C = x`. Then, `B = (x + 8) & A = (x + 15)` `:. x + x + 8 + x + 15 = 53` or `x = 10`. `A : B : C = 25 : 18 : 10`.
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Question: `Rs. 120` are divided among `A, B, C` such that `A's` share is `Rs. 20`more than `B's` and `Rs. 20` less than `C's`. What is `B's` share ?
A
`Rs. 10`

B
`Rs. 15`

C
`Rs. 20`

D
`Rs. 25`

Note: Let `C =x`. Then, `A = (x - 20)` and `B = (x - 40)`. `:. x + x - 20 + x - 40 = 120` or `x = 60`. `A : B : C = 40 : 20 : 60` `= 2 : 1 : 3`. `B's` share `= Rs. (120 xx 1/6)` `= Rs. 20`.
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Question: `A` sum of `Rs. 1300` is divided among `P, Q, R` and `S` such that : `(P's share)/(Q's share) = (Q's share)/(R's share) = (R's share)/(S's share) = 2/3`. What is `P's share` ?
A
`Rs. 320`

B
`Rs. 240`

C
`Rs. 160`

D
`Rs. 140`

Note: `P : Q = 2 : 3, Q : R = 2 : 3 = 3/2 xx 2 : 3/2 xx 3 = 3 : 9/2`. `:. P : Q : R = 2 : 3 : 9/2 = 4 : 6 : 9` And, `R : S = 2 : 3 : 9/2 xx 2 : 9/2 xx 3 = 9 : (27)/2` `:. P : Q : R : S = 4 : 6 : 9 : (27)/2 = 8 : 12 : 18 : 27`. `:. P's share = Rs. (1300 xx 8/(65))` `= Rs. 160`.
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Question: `Rs. 600` are divided among `A, B, C` so that `Rs. 40` more than `2/5`th of `A's` share, `Rs. 20` more than `2/7`th of `B's` share and `Rs. 10` more than `9/(17)`th of `C's` share may all be equal. What is `A's` share ?
A
`Rs. 150`

B
`Rs. 170`

C
`Rs. 200`

D
`Rs. 280`

Note: `2/5A + 40 = 2/7B + 20 = 9/(27)C + 10 = x`. `:. A = 5/2 (x - 40), B = 7/2 (x - 20)` and `C = (17)/9 (x - 10)`. `:. 5/2 (x - 40) + 7/2 (x - 20) + (17)/9 (x - 10) = 600` or `x = 100`. `:. A's` share `= Rs. [5/2 (100 - 40)]` `= Rs. 150`.
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Question: `Rs. 180` contained in a box consists of one rupee, `50-`paise and `25-`paise coins in the proportion of `2 : 3 : 4`. What is the number of `50-`paise coins ?
A
`120`

B
`150`

C
`180`

D
`240`

Note: Ratio of values `= 2/1 : 3/2 : 4/4` `= 2 : 3/2 : 1` `= 4 : 3 : 2`. Value of `50-`paise coins `= Rs. (180 xx 3/9)` `= Rs. 60`. Number of `50-`paise coins `= (60 xx 2)` `= 120`.
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Question: A box contains `Rs. 56` in the form of coins of one rupee, `50-` paise and `25-` paise. The number of `50-` paise coins is double the number of `25` paise coins and four times the number of one rupee coins. How many `50` paise coins are there in the box ?
A
`64`

B
`32`

C
`16`

D
Data inadequate

Note: Let rupee coins `= x, 50-`paise coins `= 4x` and `25-` paise coins `= 2x`. `:.` Ratio of these coins `x : 4x : 2x = 1 : 4 : 2`. Ratio of their values `= 1/1 : 4/2 : 2/4 = 4 : 8 : 2 = 2 : 4 : 1`. `:.` Value of `50-` paise coins `= Rs. (56 xx 4/7)` `= Rs. 32`. Number of `50-` paise coins `= 64`.
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Question: In a cash bag there are currency notes in denominations of `Rs. 20` Rs. 10` and `Rs. 5` in the ratio `3 : 4 : 5`. If the total amount in the bag is `Rs. 1000`, the number of five-rupee notes is :
A
`40`

B
`36`

C
`30`

D
`25`

Note: Ratio of the number of `Rs. 20, Rs. 10, Rs. 5` notes `= 3 : 4 : 5`. Ratio of their values `= 60 : 40 : 25 = 12 : 8 : 5`. Value of five-rupee notes `=Rs. (1000 xx 5/(25))` `= Rs. 200`. Number of five-rupee notes `= ((200 )/5) = 40`.
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Question: A purse contains one-rupee, `50-` paise, `25-` paise and `20-` paise coins in the ratio of `1 : 2 : 4 : 5`. If the total value of coins is `Rs. 400`, then the number of `20-` paise coins exceeding those of `25-` paise coins is :
A
`100`

B
`200`

C
`400`

D
`500`

Note: Ratio of values `= 1/1 : 2/2 : 4/4 : 5/5 = 1 : 1 : 1 : 1`. Value of `20` paise coins `= Rs. (400 xx 1/4) = Rs. 100`. Number of `20` paise coins `= (100 xx 5) = 500`. Value of `25` paise coins `= Rs. (400 xx 1/4) = Rs. 100`. Number of `25` paise coins `= (100 xx 4) = 400`. Difference in number of `20-` paise & `25-`paise coins `= 100`.
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Question: In a school, `10%` of the boys are same in number as `1/4`th of the girls and `10%` of the girls are same in number as `1/(25)`th of the boys. What is the ratio of boys to girls in that school ?
A
`3 : 2`

B
`5 : 2`

C
`2 : 1`

D
`4 : 3`

Note: `(10)/(100) B = 1/4 G` and `(10)/(100) G = 1/(25) B` `2B - 5G = 0 ` and `5G - 2B = 0`. `:. 2B = 5G` or `B/G = 5/2`.
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Question: `Rs. 730` were divided among `A, B, C` in such a way that if `A` gets `Rs. 3`, then `B` gets `Rs. 4` and if `B` gets `Rs. 3.50` then `C` gets `Rs. 3`. The share of `B` exceeds that of `C` by :

Question: `Rs. 53`are divided among three persons `A, B, C` in such a way that `A`gets `Rs 7` more than what `B` gets and `B` gets `Rs. 8` more than what `C`gets. The ratio of their shares is :

Question: `Rs. 120` are divided among `A, B, C` such that `A's` share is `Rs. 20`more than `B's` and `Rs. 20` less than `C's`. What is `B's` share ?

Question: `A` sum of `Rs. 1300` is divided among `P, Q, R` and `S` such that : `(P's share)/(Q's share) = (Q's share)/(R's share) = (R's share)/(S's share) = 2/3`. What is `P's share` ?

Question: `Rs. 600` are divided among `A, B, C` so that `Rs. 40` more than `2/5`th of `A's` share, `Rs. 20` more than `2/7`th of `B's` share and `Rs. 10` more than `9/(17)`th of `C's` share may all be equal. What is `A's` share ?

Question: `Rs. 180` contained in a box consists of one rupee, `50-`paise and `25-`paise coins in the proportion of `2 : 3 : 4`. What is the number of `50-`paise coins ?

Question: A box contains `Rs. 56` in the form of coins of one rupee, `50-` paise and `25-` paise. The number of `50-` paise coins is double the number of `25` paise coins and four times the number of one rupee coins. How many `50` paise coins are there in the box ?

Question: In a cash bag there are currency notes in denominations of `Rs. 20` Rs. 10` and `Rs. 5` in the ratio `3 : 4 : 5`. If the total amount in the bag is `Rs. 1000`, the number of five-rupee notes is :

Question: A purse contains one-rupee, `50-` paise, `25-` paise and `20-` paise coins in the ratio of `1 : 2 : 4 : 5`. If the total value of coins is `Rs. 400`, then the number of `20-` paise coins exceeding those of `25-` paise coins is :

Question: In a school, `10%` of the boys are same in number as `1/4`th of the girls and `10%` of the girls are same in number as `1/(25)`th of the boys. What is the ratio of boys to girls in that school ?