Ratio & Proportion, General Mathematics

Question: The third proportional to `(x^2 - y^2)` and `(x - y)` is :
A
`(x + y)/(x - Y)`

B
`(x - y)/(x + y)`

C
`x + y`

D
`x - y`

Note: Let `(x^2 - y^2) : (x - y) = (x - y) : z`. Then, `z = ((x - y)(x - y))/((x^2 - y^2))` `= ((x - Y))/((x + y))`.
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Question: The ratio of third proportional to `12` and `30` and the mean proportional of `9` and `25` is :
A
`2 : 1`

B
`5 : 1`

C
`7 : 15`

D
`9 : 14`

Note: Let `12 : 30 = 30 : x`. Then, `x = (30 xx 30)/12` ` = 75`. Also, `y = sqrt(9 xx 25)` ` = 15`. `:.`Required ratio `= x : y` `= 75 : 15` `= 5 : 1`.
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Question: In a ratio which is equal to `3 : 4`, if the antecedent is `12`, then consequent is :
A
`9`

B
`16`

C
`20`

D
`24`

Note: `3/4 = (12)/x` `iff 3x = 48` `iff x = 16`.
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Question: If `0.4` of a number is equal to `0.06` of another number, then the retio of the numbers is :
A
`2 : 3`

B
`3 : 4`

C
`3 : 20`

D
`20 : 3`

Note: `0.4A = 0.06B` `iff A/B = (0.06)/(0.4)` ` = 6/(40)` ` = 3/(20)`.
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Question: A fraction which bears the same ratio to `1/(27)` that `3/(11)` does to `5/9`, is :
A
`1/(55)`

B
`55`

C
`1/(11)`

D
`3/(11)`

Note: `x : 1/(27) = 3/(11) : 5/9` `iff 5/9 x = 1/(27) xx 3/(11)` `:. 5/9 x = 1/(99)` or, `x = (1/(99) xx 9/5)` `= 1/(55)`.
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Question: If `a + b : b + c : c + a = 6 : 7 : 8` and `a + b + c = 14`, then the value of `c` is :
A
`6`

B
`7`

C
`8`

D
`14`

Note: Let `(a + b) = 6k`, `b + c = 7k` and `c + a = 8k`. Then,`2(a + b + c) = 21k` or `2 xx 14 = 21k` or `k = 4/3`. `:. a + b = (6 xx 4/3) = 8`. So, `c = (a + b + c) - (a + b)` `= (14 - 8)` `= 6`.
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Question: If `a/3 = b/4 = c/7`, then `(a + B + c)/c` is equal to :
A
`7`

B
`2`

C
`1/2`

D
`1/7`

Note: `a/3 = b/4 = c/7 = k`. Then, `a = 3k`, `b = 4k` and `c = 7k`. `:. (a + b + c)/c` `= (3k + 4k + 7k)/7k` `= (14k)/7k` `= 2`.
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Question: If `x/5 = y/8`, then `(x + 5) : (y + 8)` is equal to :
A
`3 : 5`

B
`13 : 8`

C
`8 : 5`

D
`5 : 8`

Note: Let `x/5 = y/8 = k`. Then, `x = 5k` and `y = 8k`. `:. (x + 5)/(y + 8)` `= (5k + 5)/(8k + 8)` `= (5(k + 1))/(8(k + 1)` `= 5/8`.
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Question: If`x : y = 6 : 5`, then `(5x + 3y) : (5x - 3y)` is equal to :
A
`2 : 1`

B
`3 : 1`

C
`5 : 3`

D
`5 : 2`

Note: Given : `x/y = 6/5`. `:. (5x + 3y)/(5x - 3y)` `= (5(x/y) + 3)/(5(x/y) - 3)` `= (5 xx 6/5 + 3)/(5 xx 6/5 - 3)` `= 9/3` `= 3/1`.
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Question: If the ratio of `A` to `B` is `9` times the ratio of `B` to `A`, then `A/B` could be :
A
`9`

B
`3`

C
`1/3`

D
`1/9`

Note: `A/B = (9B)/A` `iff A^2/B^2 = 9/1` `iff A/B = 3/1`.
1. Report

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Question: The third proportional to `(x^2 - y^2)` and `(x - y)` is :

Question: The ratio of third proportional to `12` and `30` and the mean proportional of `9` and `25` is :

Question: In a ratio which is equal to `3 : 4`, if the antecedent is `12`, then consequent is :

Question: If `0.4` of a number is equal to `0.06` of another number, then the retio of the numbers is :

Question: A fraction which bears the same ratio to `1/(27)` that `3/(11)` does to `5/9`, is :

Question: If `a + b : b + c : c + a = 6 : 7 : 8` and `a + b + c = 14`, then the value of `c` is :

Question: If `a/3 = b/4 = c/7`, then `(a + B + c)/c` is equal to :

Question: If `x/5 = y/8`, then `(x + 5) : (y + 8)` is equal to :

Question: If`x : y = 6 : 5`, then `(5x + 3y) : (5x - 3y)` is equal to :

Question: If the ratio of `A` to `B` is `9` times the ratio of `B` to `A`, then `A/B` could be :