Simple Interest
 

  1. Question: A sum of money trebles itself in `15` years `6` month. In how many years would it double itself ?

    A
    `6` years `3` month

    B
    `7` years `9` month

    C
    `8` years `3` month

    D
    `9` years `6` month

    Note: Let sum = x. Then,S.I.`= 2x &`Time `= 31/2` years Rate` = ((100 xx 2x)/x xx 2/31)%` `= (400/31)%` :. Time` = ((100 xx x)/x xx 31/400)` years. `= 7` years`9` month
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  2. Question: Simple interest on a certain sum at a certain rate is `9/16` of the sum. If the numbers representing rate percent and time in years be equal, then the rate is :

    A
    `5 1/2%`

    B
    `6 1/25`

    C
    `6 1/4%`

    D
    `7 1/2%`

    Note: Let sum = x.Then, S.I.`= 9x/16`. Let time = n years & rate = n% `:. n = 100 xx (9x)/16 xx 1/x xx 1/n` `or n^2 = 900/16` `or n = 30/4` `= 7 1/2%`
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  3. Question: The simple interest on a sum of money is `1/9` of the sum. The number of years is numerically equal to the rate percent per annum. The rate percent per annum is :

    A
    `3 1/3`

    B
    `5`

    C
    `6 2/3`

    D
    `10`

    Note: Let sum = x.Then, S.I.`= x/9` Let time = n years and rate = n% Then, n`= 100 xx x/9 xx 1/(x xx n)` `or n^2 = 100/9` `or n = 10/3` `= 3 1/3%`
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  4. Question: Consider the following ststements : If a sum of money is lent at simple interest, then the 1.money gets doubled in `5` years if the rate of interest is `16 2/3%` 2.money gets doubled four times if the rate of interest is `20%` 3.money becomes four times in `10`years if it gets doubled in `5` years. of these statements,

    A
    `1` and `3` are correct

    B
    `3` alone is correct

    C
    `2` alone is correct

    D
    `2` and `3` are correct

    Note: Let sum be x.Then,S.I =x 1. Time`= (100 xx x)/(x xx 50/3)` `= 6` years (False) 2.Time `= (100 xx x)/(x xx 20)` `= 5`years (True) 3. Suppose sum = x. Then, S.I = x & Times `= 5` years Rate`= ((100 xx x)/(x xx 5))%` `= 20%` Now sum = x,S.I`.= 3x & Rate = 20%` :. Time` =((100 xx 3x)/(x xx 20))`years `= 15` years (false) So,`2` alone is correct.
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  5. Question: A Sum of Rs. `10` is lent to be returned in `11` monthly instalments of Rs. `1` each interest begin simple. The rate of interest is :

    A
    `9 1/11%`

    B
    `10%`

    C
    `11%`

    D
    `21 9/11%`

    Note: Rs. `10` + S.I.on Rs. `10`for `11` months `= Rs. 11` + S.I. on Re 1. for `110` months `= Rs. 11` + S.I. on Re. `11` + S.I. on Re` 1`for `55` months S.I. on Re `1` for `55` months = Re `1`. :. Rate`= ((100 xx 12)/(1 xx 55))%` `= 21 9/11%`
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  6. Question: What annual payment will discharge a debt of Rs. `580` due in `5` years the rate being `8%` per annum ?

    A
    `Rs. 65.60`

    B
    `Rs. 100`

    C
    `Rs. 166.40`

    D
    `Rs. 12`

    Note: Let the annual instalment be Rs. x. Then, `[x + ((x xx 4 xx 8)/100)] +[ x + ((x xx 3 xx 8)/100)] x + ((x xx 2 xx 8)/100)] + [ x + ((x xx 2 xx 8)/100)] + x = 580` `or (33x)/25 + (31x)/25 + (29x)/25 + (27x)/25 + x = 580` `or x = 100`.
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  7. Question: The simple interest on a sum of money will be Rs.`600` after `10` years. If the principal is trebled after `5` years, what will be the total interest at the end of the tenth year ?

    A
    `Rs. 600`

    B
    `Rs. 900`

    C
    `Rs. 1200`

    D
    Date inadequate

    Note: Let sum = x,S.I. Rs.` 600`, TIme = `10` years Rate` = ((100 xx 6000)/(x xx 10))` `= (6000/x)%` S.I. for first `5` years `= Rs. ((x xx 5 xx 6000)/(x xx 100))` `= Rs. 300` S.I. for first `5` years `= Rs. (3x xx 5 xx 6000/(x xx 100))` `= Rs. 900`. :. Total interest` = Rs. 1200`.
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  8. Question: The rate of simple interest on a sum of money is `6%`p.a for the first `3` years `8%`p.a .for the next `5` years and `10%` p.a. for the period beyond `8` years. If the simple interest accrued by the sum for a total period of `10` years is Rs. 1560`,what is the sum ?

    A
    `Rs. 1500`

    B
    `Rs. 2000`

    C
    `Rs. 3000`

    D
    Date inadeequate

    Note: Let the sum be Rs.x.Then. `(x xx 6 xx 3)/100 + (x xx 8 xx 5)/100 + (x xx 10 xx 2)/100 = 1560` `or 78x = 156000` `or x = 2000`.
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  9. Question: The rate of interest on a sum of money is `4%`p.a. for the first `2` years, `6%` p.a. for the next `3` years and `8%` p.a. for the period beynond `5` years, If the simple interest accrued by the sum for a total period of `8` years is Rs. `1280`, what is the sum ?

    A
    `Rs. 1523`

    B
    `Rs. 1680`

    C
    `Rs. 2560`

    D
    `Rs. 2840`

    Note: Let the sum be .x. Then, `(x xx 4 xx 2)/100 + (x xx 6 xx 3)/100 + (x xx 8 xx 3)/100 = 1280` `or 50x = 1280 xx 100` `:. x = 2560`.
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  10. Question: How long will it take a sum of money invested at `5%` p.a. S.I.to incrcease its value by `40%` ?

    A
    `5 years`

    B
    `6 years`

    C
    `7 years`

    D
    `8 years`

    Note: Let the sum be x. Then, amount `= 140/100 x = 7x/5`. :. S.I. = ((7x)/5 - x)` `= (2x)/5`. Thus, sum = x, S.I. `= (2x)/5 & Rate = 5%` :. Time`= (100 xx (2x)/5 xx 1/(x xx 5)` `= 8 years`
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