Simplification
 

  1. Question: `3/8` is what part of `1/12 ?`

    A
    `3/7`

    B
    `1/12`

    C
    `4/3`

    D
    None of these

    Note: Let,x of `1/12 = 3/8` Then,`x/12 = 3/8⇔` `x = (12 xx 3/4) = 9/2`
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  2. Question: `3 1/4 + 4 1/6 + ? + 1/4 =10`

    A
    `2 1/6`

    B
    `4 1/3`

    C
    `1 1/3`

    D
    `2 1/3`

    Note: Let ,`13/4 + 25/6 + x + 1/4 =10`. Then,`x = 10 - (13/4 + 25/6 + 1/4)` or `x =10 - ((39 + 50 + 3)/12)` `= (10 - 92/12)` `= ((120 - 92)/12)` `= 28/12` `= 7/3` `= 2 1/3`.
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  3. Question: `4 1/2 + 3 1/6 + ? + 2 1/3 = 13 2/5`

    A
    `3 2/5`

    B
    `1 2/5`

    C
    `4 1/5`

    D
    `4 1/6`

    Note: Let,`9/2 + 19/6 + x + 7/3` `= 67/5`. Then,`x = 67/5` `= (9/2 + 19/6 + 7/3)` or `x = 67/5 - ((27 + 19 + 14)/6)` `= (67/5 - 60/6)` `= (67/5 - 10)` `= 17/5` `= 3 /2/5`
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  4. Question: `15 2/3 xx 3 1/6 + 6 1/3 = 11 7/18 + ?`

    A
    `39 5/9`

    B
    `137 4/9`

    C
    `29 7/9`

    D
    None of these

    Note: Let,`47/3 xx 19/6 + 19/3` `= 205/18 + x`. Then,`893/18 + 19/3` `= 205/18 + x` or`x= (893/18 + 19/3) - 205/18` or `x = ((893 + 114)/18) - 205/18` `= ((1007 - 205)/18)` `= (802/18)` `= 44 5/9`.
    1. Report

  5. Question: `5/6 ÷ 6/7 xx ? - 8/9 ÷ 1 3/5 + 3/4 xx 3 1/3 = 2 7/9`

    A
    `7/6`

    B
    `6/7`

    C
    `1`

    D
    None of these

    Note: Let,`5/6 ÷ 6/7 xx x - 8/9 ÷ 8/5 + 3/4 xx 10/3` `= 25/9` Then,`5/6 xx 7/6 xx x - 8/9 xx 5/8 + 5/2` `= 25/9` or ` 35/36 x - 5/9 + 5/2` `= 25/9` or`35/36 x` `= 25/9 + 5/9 - 5/2` or`35/36 x` `= 10/3 - 5/2` `= 5/6` or`x 5/6 xx 36/35` `=6/7`.
    1. Report

  6. Question: By how much is two third of `57` more than one third of `90 ?`

    A
    `8`

    B
    `38`

    C
    `30`

    D
    `28`

    Note: Requied excess, `= (2/3 xx 57 - 1/3 xx 90)` `= (38 - 30)` `= 8`.
    1. Report

  7. Question: If `45 - [28 - {37 - (15 - *)}] = 58`,Then * is equal to.

    A
    `-19`

    B
    `19`

    C
    `29`

    D
    `-29`

    Note: Let,`45 - [28 - {37 - (15 - x )}]= 58`. `Then 45 - [28 - {37 - 15 + x}] = 58` or `45 - [28 - (22 + x}]= 58` or `45 - [28 - 22 - x]= 58` or `45 - [6 - x]= 58` or `45 - 6 + x = 58` or ` 39 + x = 58` or `x = (58 - 39)= 19`.
    1. Report

  8. Question: The missing figures at * and ** in `(9 3/**) xx (***** 7/9)= 16 2/3` will respectively be .

    A
    `1,8`

    B
    `5,1`

    C
    `8,1`

    D
    `7,2`

    Note: Substituting the given values ,we have ` 9 3/8 xx 1 7/9` `= 75/8 xx 16/9` `= 150/9` `= 50/3` `= 16 2/3`.
    1. Report

  9. Question: `8 1/4 - 4 1/5 + 2.8 + 4/? - 2.32 = 5.33`

    A
    `5`

    B
    `.5`

    C
    `.05`

    D
    Nones of these

    Note: Let,`33/4 - 21/5 + 28/10 + 4/x - 232/100 = 533/100` Then,`4/x = 533/100 + 232/100 + 21/5 - 33/4 - 28/10` or` 4/x = 765/100 + (84 - 165 - 56)/20` or `4/x = 765/100 - 137/20` or`4/x = (765 - 685)/20` or`4/x = 80/20` `= 4/1` So,`x = 1`.
    1. Report

  10. Question: `6 2/3 of 7.26 ÷ .45 of ? = 8 32/117`

    A
    `1/13`

    B
    `13`

    C
    `13 1/9`

    D
    None of these

    Note: Let,`20/3 of 726/100 ÷ 45/100 of x = 968/117` `or 242/5 ÷ (45x)/100` `= 968/117` `0r 242/5 xx 100/(45x)` `= 968/117` `or x = 242/5 xx 100/45 xx 117/968` `or x = 13`
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