Ratio & Proportion
 

  1. Question: Which of the following ratios is the greatest ?

    A
    `7 : 15`

    B
    `15 : 23`

    C
    `17 : 25`

    D
    `21 : 29`

    Note: `7/(15) = 0.466`, `(15)/(23) = 0.652`, `(17)/(25) = 0.68` & `(21)/(29) = 0.724`. Clearly, `0.724`is greatest and hence `21 : 29` is greatest.
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  2. Question: Two whole numbers whose sum is `72` cannot be in the ratio :

    A
    `5 : 7`

    B
    `3 : 5`

    C
    `4 : 5`

    D
    `3 : 4`

    Note: The sum of the ratio terms must divide `72` So, the ratio cannot be `3 : 4`.
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  3. Question: If a carton containing a dozen mirrors is dropped, which of the following cannot be the ratio of broken mirrors to unbroken mirrors ?

    A
    `2 : 1`

    B
    `3 : 1`

    C
    `3 : 2`

    D
    `7 : 5`

    Note: For dividing `12` into two whole numbers, the sum of the terms of the ratio must be a factor of `12`. So, they cannot be in the ratio `3 : 2`.
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  4. Question: The ratio of two numbers is `3 : 4` and their sum is `420`. The greater of the two numbers is :

    A
    `175`

    B
    `200`

    C
    `240`

    D
    `315`

    Note: Required number `= (420 xx 4/7)` `= 240`.
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  5. Question: The ratio between two numbers is `3 : 4` and their `1`c.m is `180`. The first number is :

    A
    `60`

    B
    `45`

    C
    `20`

    D
    `15`

    Note: Let the numbers be `3x`and `4x`. Then, their `1`c.m `= 12x`. Now, `12x = 180` `iff x = 15`. `:.`First number `= 45`.
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  6. Question: The L.C.M. and H.C.F. of two numbers `x` and `y` are `l` and `h` repectively. Then,

    A
    `l : h = x : y`

    B
    `x : h = l : y`

    C
    `x : l = y : h`

    D
    `x : h = y : l`

    Note: Product of numbers = Product of their H.C.F. & L.C.M. `:. xy = lh` `iff x/h = l/y` `iff x : h = l : y`.
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  7. Question: `A` and `B` together have Rs. `1210` with them. If `4/(15)` of `A`'s amount is equal to `2/5` of `B`'s amount, how much amount does `B` have ?

    A
    `Rs. 466`

    B
    `Rs. 484`

    C
    `Rs. 550`

    D
    `Rs. 664`

    Note: `4/(15) A = 2/5 B` `=> A/B = (2/5 xx (15)/4) = 3/2`. Thus, `A : B = 3 : 2`. `:. B`'s share `= R's (1210 xx 2/5)` `= Rs. 484`.
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  8. Question: Five bananas and four apples cost as much as three bananas and seven apples. The ratio of the cost of one banana to that of one apple is :

    A
    `3 : 2`

    B
    `4 : 3`

    C
    `3 : 4`

    D
    `1 : 3`

    Note: Let the cost of each banana be `x` paise and that of each apple by `y` paise. Then, `5x + 4y = 3x + 7y ` `iff 2x = 3y` `iff x/y = 3/2`. `:.` Required ratio is `3 : 2`.
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  9. Question: The salaries of `A, B,` and `C` are in the ratio of `1 : 2 : 3`. The salary of `B` and `C` together is Rs. `6000`. By what percent is the salary of `C` more than that of `A` ?

    A
    `100%`

    B
    `200%`

    C
    `300%`

    D
    `600%`

    Note: Let the salaries of `A, B, C` be `x, 2x` and `3x` respectively. Then, `2x + 3x = 6000` `iff x = 1200`. `:. A's`salary `= Rs. 1200, B's ` salary `= Rs. 2400`, and `C's` salary `= Rs. 3600`. `:.` Excess of `C's` salary over `A's = ((2400)/(1200) xx 100)%` `= 200%`
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  10. Question: The average age of three boys is `25` years and their ages are in the proportion `3 : 5 : 7`. The age of the youngest boy is :

    A
    `21` years

    B
    `18` years

    C
    `15` years

    D
    `9` years

    Note: Total age of 3 boys `= (25 xx 3)`years `= 75` years. `:.` Age of the youngest `= (75 xx 3/(15))` `= 15` years.
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