General Mathematics
 

  1. Question: If the difference between the compound interest, compounded half yearly and the simple interest on a sum at `10%` per annum for one year is Rs.`25`,the sum is :

    A
    `Rs. 9000`

    B
    `Rs. 9500`

    C
    `Rs. 10000`

    D
    `Rs. 10500`

    Note: Let the sum be Rs.x. Then, C.I.`= x (1 + 5/100)^2 - x` `= ((441x)/400 - x)` `= (41x)/400` S.I.`= (x xx 10 xx 1)/100` `= x/10` (C.I) - (S.I)`= (41x)/400 - x/10` `= x/400` `:. x/400 = 25` `or x 10000`.
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  2. 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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  3. Question: A man borrowed Rs. `800`at `10%` per annum simple interest and immediately lent the whole sum at `10%` per annum compound interest. What dose he gain at the end of `2` years ?

    A
    `Rs. 6`

    B
    `Rs. 8`

    C
    `Rs. 10`

    D
    `Rs. 12`

    Note: C.I.= Rs.` [ 800 xx (1 + 10/100)^2 - 800]` `= Rs. 168.` S.I. Rs.`((800 xx 10 xx 2)/100)` `= Rs. 160` Gain = (C.I) - (S.I) `= Rs. (168 - 160)` `= Rs.= 8`
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  4. Question: On what sum of money will the simple interest for `3` years at `8%` per annum be half of the compound interest on Rs.`400` for `2` years at `10%` per annum ?

    A
    `Rs. 125`

    B
    `Rs. 150`

    C
    `Rs. 175`

    D
    `Rs. 200`

    Note: C.I. on Rs.`400` for `2` years at `10%` p.a. `= Rs. [400 xx (1 + 10/100)^2 - 400]` `= Rs. 84` required S.I.`= 1/2 xx Rs. 84` `= Rs. 42`. Now S.I.` = Rs. 42,`Time`= 3`years & Rate` = 8%` `:. sum` `= Rs.((100 xx 42)/(3 xx 8))` `= Rs. 175`
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  5. 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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  6. 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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  7. Question: The compound interest on a certain sum at `5%` per annum for `2` years is Rs.`328`.The simple interest for sum at the same rate and for the same period will be :

    A
    `Rs. 320`

    B
    `Rs. 322`

    C
    `Rs. 325`

    D
    `Rs. 326`

    Note: Let the sum be.x.Then, C.I` = x (1 + 5/100)^2 - x` `= ((441x)/400 - x)` `= (41x)/400` `:. (41x/400` `= 328` `or x = (328 xx 400)/41` `= 3200` `:. S.I.Rs. ((3200 xx 5 xx 2)/100` `=Rs. 320`.
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  8. 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`.
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  9. Question: The compound interest on Rs.`5600` for `1 1/2` years at `10%` per annum, compound annumaly is :

    A
    `Rs. 882.70`

    B
    `Rs. 873.50`

    C
    `Rs. 868`

    D
    `Rs. 840`

    Note: Not available
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  10. Question: The compound interest on Rs.`20480` at `6 1/4%` per annum for `2` years `73` days is :

    A
    `Rs. 3000`

    B
    `Rs. 3131`

    C
    `Rs. 2929`

    D
    `Rs. 3636`

    Note: Time`= 2 73/365` years `= 2 1/5` years :. Amount` = Rs. [ 20480 xx (1 + 25/(4 xx 100)^2 (1 + (1/5 xx 25/4)/100)]` `= Rs. (20480 xx 17/16 xx 17/16 xx 81/80)` `= Rs. 23409`. :. C.I.` Rs. (23409 - 20480)` `= Rs. 2929`.
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