Ratio & Proportion, General Mathematics

Question: `94` is divided into two parts in such a way that fifty part of first and the eighth part of the second and in the ratio `3 : 4`. The first part is :
A
`27`

B
`30`

C
`36`

D
`48`

Note: `(A / 5)/(B / 8) = 3/4` `iff A/5 xx 8/B = 3/4` `iff A/B = 3/4 xx 5/8` `= (15)/(32)`. Thus, `A : B = 15 : 32`. `:.` First part `= (94 xx (15)/(47))` `= 30`.
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Question: `33 1/3%`of a man's output is equal to `50%` of a second man's daily output. It the second man turns out `1500` screws daily, then the first man's output in terms of making screws is:
A
`500`

B
`1000`

C
`2000`

D
`2250`

Note: `(100)/(3 xx 100) A = (50)/(100) B` `iff 1/3 A = 1/2 B`. `B = 1500`. So, `1/3 A = 1/2 xx 1500 = 750`. `:. A = (3 xx 750)` `= 2250`
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Question: The sum of three numbers is `98`. If the ratio of the first to the second is `2 : 3` and that of second to the third is `5 : 8`, then the second number is :
A
`20`

B
`30`

C
`48`

D
`58`

Note: Let the numbers be `A, B` and `C`. Then, `A : B = 2 : 3` and `B : C = 5 : 8` `= 3/5 xx 5 : 3/5 xx 8` `= 3 : (24)/5`. `:. A : B : C = 2 : 3 : (24)/5` `= 10 : 15 : 24`. Second number `= (98 xx (15)/(49))` `= 30`.
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Question: If three numbers in the ratio `3 : 2 : 5` be such that the sum of their squares is `1862`, the middle number will be :
A
`7`

B
`14`

C
`21`

D
`35`

Note: Let the numbers be `3x, 2x` and `5x`. Then, `9x^2 + 4x^2 25x^2 = 1862` `iff 38x^2 = 1862` `iff x^2 = 49` `iff x = 7`. `:.`Second number `= 2x` `= 14`.
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Question: Some money is divided among three persons `A, B, C` in such a way that `5` time `A's`share, `3` times `B's` share and `2` times `C's` share are all equal. The ratio between `A, B` and `C's` shares is :
A
`5 : 3 : 2`

B
`2 : 2 : 5`

C
`15 : 10 : 6`

D
`6 : 10 : 15`

Note: `5A = 3B = 2C = k`. Then, `A = k/5, B = k/3 & C = k/2`. `:. A : B : C = k/5 : k/3 : k/2` `= 1/5 : 1/3 : 1/2` `= 6 : 10 : 15`.
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Question: `A` sum of Rs. `427` is to be divided among `A, B` and `C` such that `3` times `A's` share, `4` times `B's share and `7`times `C's` share are all equal. The share of `C` is :
A
`Rs. 84`

B
`Rs. 147`

C
`Rs. 196`

D
`Rs. 240`

Note: `3A = 4B = 3C = k`. Then, `A = k/3, B = k/4` and `C = k/7`. `:. A : B : C = k/3 : k/4 : k/7` `= 28 : 21 : 12`. `:. C's` share `= Rs. (427 xx (12)/(61))` `= Rs. 84`.
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Question: If `Rs. 1540` be divided amongst `A, B, C` in such a way that the share of `B` is equal to `3/(11)` of what `A` and `C` together receive. Then, `B's` share will be :
A
`Rs. 330`

B
`Rs. 420`

C
`Rs. 880`

D
`Rs. 1210`

Note: `B = 3/(11)(A + B)`. So, `B : (A + C) = 3 : 11`. `:. B's`share `= Rs. (1540 xx 3/(14))` `= Rs. 330`.
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Question: `Rs.1870`are divided into three parts in such a way that half of the first part, one-third of the second part and one-sixth of the third part are equal. The third part is :
A
`Rs. 510`

B
`Rs. 680`

C
`Rs. 850`

D
`Rs. 1020`

Note: `A/2 = B/3 = C/6 = k`. Then `A = 2k, B = 3k` and `C= 6k`. `:. A : B : C = 2k : 3k : 6k` `= 2 : 3 : 6`. `:.` Third part `= Rs. (1870 xx 6/(11))` `= Rs. 1020`.
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Question: `Rs. 2040` are divided among `A, B, C` such that `A` gets `1/3` of what `B` gets and `B` gets `1/4` of what `C` gets. Then `B's` share is :
A
`Rs. 180`

B
`Rs. 240`

C
`Rs. 360`

D
`Rs. 480`

Note: Suppose `C` gets `Re 1`. Then, `B` gets `Re 1/4`. `A` gets `= 2/3` of `Re = 1/4 = Re 1/6`. `:. A : B : C = 1/6 : 1/4 : 1` `= 2 : 3 : 12`. `:. B's` share `= Rs. (2040 xx 3/(17))` `= Rs. 360`.
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Question: A sum of money is divided among `A, B, C` such that to each rupee `A` gets, `B` gets, `65` paise and `C` gets `35` paise. If `C`'s share is `Rs. 28`, the sum is :
A
`Rs. 120`

B
`Rs. 140`

C
`Rs. 160`

D
`Rs. 180`

Note: `A : B : C = 100 : 65 : 35` `= 20 : 13 : 7`. `:. 7 : 40 = 28 : X` or `X = (40 xx 28)/7` `= 160`. `:.` Sum `= Rs. 160`.
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Question: `94` is divided into two parts in such a way that fifty part of first and the eighth part of the second and in the ratio `3 : 4`. The first part is :

Question: `33 1/3%`of a man's output is equal to `50%` of a second man's daily output. It the second man turns out `1500` screws daily, then the first man's output in terms of making screws is:

Question: The sum of three numbers is `98`. If the ratio of the first to the second is `2 : 3` and that of second to the third is `5 : 8`, then the second number is :

Question: If three numbers in the ratio `3 : 2 : 5` be such that the sum of their squares is `1862`, the middle number will be :

Question: Some money is divided among three persons `A, B, C` in such a way that `5` time `A's`share, `3` times `B's` share and `2` times `C's` share are all equal. The ratio between `A, B` and `C's` shares is :

Question: `A` sum of Rs. `427` is to be divided among `A, B` and `C` such that `3` times `A's` share, `4` times `B's share and `7`times `C's` share are all equal. The share of `C` is :

Question: If `Rs. 1540` be divided amongst `A, B, C` in such a way that the share of `B` is equal to `3/(11)` of what `A` and `C` together receive. Then, `B's` share will be :

Question: `Rs.1870`are divided into three parts in such a way that half of the first part, one-third of the second part and one-sixth of the third part are equal. The third part is :

Question: `Rs. 2040` are divided among `A, B, C` such that `A` gets `1/3` of what `B` gets and `B` gets `1/4` of what `C` gets. Then `B's` share is :

Question: A sum of money is divided among `A, B, C` such that to each rupee `A` gets, `B` gets, `65` paise and `C` gets `35` paise. If `C`'s share is `Rs. 28`, the sum is :