Ratio & Proportion, General Mathematics

Question: The incomes of `A, B, C` are in the ratio of `7 : 9 : 12` and their spendings ate in the ratio of `8 : 9 : 15`. If `A` saves `1/4`th of his income, then the savings of `A, B, C` are in the ratio of :
A
`56 : 99 : 69`

B
`99 : 56 : 69`

C
`69 : 56 : 99`

D
`99 : 69 : 56`

Note: Let their incomes be `7x, 9x` and `12x` and their spendings be `8y, 9y` and `15y`. Theb, their saving are `(7x - 8y), (9x - 9y) & (12x - 15y)`. Now, `7x - 8y = (7x)/4` or `21x = 32y` or `x/y = (32)/(21)`. `:. (7x - 8y)/(9x - 9y) =(7 (x/y) - 8)/(9 (x/y) - 9)` `= (7 xx ((32)/(21)) - 8)/(9 xx ((32)/(21)) - 9)` `= 8/3 xx 7/(33)` `= (56)/(99)`. `(9x - 9y)/(12x - 15y) = (9 (x/y) - 9)/(12 (x/y) - 15)` `= (9 xx (32)/(21) - 9)/(12 xx (32)/(21) - 15)` `= (33)/(23)` `= (99)/(69)`. `:.` Ratio of savings `= 56 : 99 : 69`.
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Question: If `76` is divided into four parts proportional to `7, 5, 3, 4,` the smallest part is :
A
`12`

B
`15`

C
`16`

D
`19`

Note: Given Ratio is `7 : 5 : 3 : 4`. `:.` Smallest part `= (76 xx 3/(19))` `= 12`.
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Question: Ramlal divided two sums of money among his four sons Anil, Rahul, Deepak and Sanjeev. The first sum is divided in the ratio `4 : 3 : 2 : 1` and second in the ratio `5 : 6 : 7 : 8`. If the second sum is twice the first, the largest total is received by :
A
Anil

B
Rahul

C
Deepak

D
Sanjeev

Note: Let their parts in first sum be `4x, 3x, 2x` and `x`and let their parts in second sum be `5y, 6y, 7y` and `8y`. `:. 2(4x + 3x + 2x + x) = (5y + 6y + 7y + 8y)` or `20x = 26y` or `x = (13)/(10)y`. `:. A = 4x + 5y` `= 4 xx (13)/(10)y + 5y` `= (102y)/(10)` `= 10.2y,` `R = 3x + 6y` `= 3 xx (13)/(10)y + 6y` `= (99y)/(10)` `= 9.9y,` `D = 2x + 7y` `= 2 xx (13)/(10)y + 7y` `= (96y)/(10)` `= 9.6y,` `S = x + 8y` `= (13)/(10)y + 8y` `=(93y)/(10)` `= 9.3y`. So, Anil received the largest total.
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Question: An ornament weighs `12.5` gms of which `2.5` gm is pure silver and the rest alloy. The ratio of pure silver to alloy is :
A
`1 : 4`

B
`1 : 5`

C
`4 : 1`

D
`4 : 5`

Note: pure silver : Alloy `= 2.5 : (12.5 -2.5)` `= 2.5 : 10` `= 1 : 4`.
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Question: The marks obtained by Praveen and Vijay are in the ratio of `4 : 5`and those obtained by Vijay and Suresh are in the ratio of `3 : 2`. The marks obtained by Praveen and Suresh are in the ratio of :
A
`2 : 1`

B
`5 : 3`

C
`6 : 5`

D
`5 : 6`

Note: `P : V = 4 c: 5` and `V : S = 3 : 2` `P/V = 4/5` and `V/S = 3/2`, so, `P/S = P/V xx V/S` `= 4/5 xx 3/2` `= 6/5`.
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Question: Anshul got twice as many marks in English as in Science. His total marks in English, Science and Maths are `180`. If the proportion of his marks in English and Maths is `2 : 3`, what are his marks in Science ?
A
`15`

B
`30`

C
`60`

D
`90`

Note: `E = 2S, E + S + M = 180` `iff E + 1/2E + M = 180` `:. 3E + 2M = 360` and `E/M = 2/3` or `M = 3/2E.` `:. 3E + 2 xx 3/2E = 360` or `E = 60.` `:. S = 1/2E = 1/2 xx 60` `= 30`.
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Question: Two numbers are in the ratio `3 : 4` and the product of their L.C.M. and H.S.C. is `10800`. The sum of the numbers is :
A
`180`

B
`210`

C
`225`

D
`240`

Note: Let the numbers be `3x` and `4x`. Then, `3x xx 4x = 10800` `iff 12x^2 = 10800` `iff x^2 = 900` `iff x = 30`. `:.` Sum of numbers `= 7x` `=7 xx 30` `= 210`.
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Question: The ages of `X` and `Y` are in the ratio of `3 : 1`. Fifteen years hence, the ratio will be `2 : 1`. Their present ages (in years) are :
A
`30, 10`

B
`45, 15`

C
`21, 7`

D
`60, 20`

Note: Let the ages of `X` and `Y` be `3x` and `x`. `(3x + 15)/(X + 15) = 2/1` or `3x + 15 = 2x + 30` or `x = 15`. `:.` Present ages of `X` and `Y` are `45` years and `15` years respectively.
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Question: The ratio of the number of boys and girls in a school is `3 : 2`. It `20%` of the boys and `25%` of the girls are scholarship holders, the percentage of the school students who are not scholarship holders is :
A
`56`

B
`70`

C
`78`

D
`80`

Note: Let boys `= 3x` & girls `= 2x`. Number of those who are not scholarship holders `= 80% of 3x + 75% of 2x` `=((80)/(100) xx 3x + (75)/(100) xx 2x)` `=(39x)/(10)`. `=(78)/(100) xx (5x)` `= 78%` of the total.
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Question: Gold is `19` times as heavy as water and copper is `9` times as heavy as water. In what ratio should these be mixed to get an alloy `15` times as heavy as water ?
A
`1 : 1`

B
`2 : 3`

C
`1 : 2`

D
`3 : 2`

Note: Let `1` gm of gold be mixed with `x` gm of copper to give `(1 + x)` gm of alloy. Now, `1 G = 19 W, 1C = 9W & Alloy = 15 W` `1` gm gold ` + x ` gm Copper `= (1 + x)`gm alloy. `:. 19 W + 9 Wx = (1 + x) xx 15W` or ` x = (4W)/(6W) = 2/3`. So, the ratio of gold and copper is `1 : 2/3` or `3 : 2`.
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Question: The incomes of `A, B, C` are in the ratio of `7 : 9 : 12` and their spendings ate in the ratio of `8 : 9 : 15`. If `A` saves `1/4`th of his income, then the savings of `A, B, C` are in the ratio of :

Question: If `76` is divided into four parts proportional to `7, 5, 3, 4,` the smallest part is :

Question: Ramlal divided two sums of money among his four sons Anil, Rahul, Deepak and Sanjeev. The first sum is divided in the ratio `4 : 3 : 2 : 1` and second in the ratio `5 : 6 : 7 : 8`. If the second sum is twice the first, the largest total is received by :

Question: An ornament weighs `12.5` gms of which `2.5` gm is pure silver and the rest alloy. The ratio of pure silver to alloy is :

Question: The marks obtained by Praveen and Vijay are in the ratio of `4 : 5`and those obtained by Vijay and Suresh are in the ratio of `3 : 2`. The marks obtained by Praveen and Suresh are in the ratio of :

Question: Anshul got twice as many marks in English as in Science. His total marks in English, Science and Maths are `180`. If the proportion of his marks in English and Maths is `2 : 3`, what are his marks in Science ?

Question: Two numbers are in the ratio `3 : 4` and the product of their L.C.M. and H.S.C. is `10800`. The sum of the numbers is :

Question: The ages of `X` and `Y` are in the ratio of `3 : 1`. Fifteen years hence, the ratio will be `2 : 1`. Their present ages (in years) are :

Question: The ratio of the number of boys and girls in a school is `3 : 2`. It `20%` of the boys and `25%` of the girls are scholarship holders, the percentage of the school students who are not scholarship holders is :

Question: Gold is `19` times as heavy as water and copper is `9` times as heavy as water. In what ratio should these be mixed to get an alloy `15` times as heavy as water ?