1. Question:`2 - [3 - {6 - { (5 - bar4 - 3) } ]` 

    Answer
    Given Expression ,
    
    ` = 2 - [3 - { 6 - (5 - 1) } ]`
    
    `= 2 - [3 - {6 - 4} ]`
    
    `= [3 - 2]`
    
    `= (2 - 1)`
    
    `= 1`.

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  2. Question:`[3 1/4 ÷ {1 1/4 - 1/2 (2 1/2 - bar1/4 - 1/6)}]` 

    Answer
    `[13/4 ÷ { 5/4 - 1/2 (5/2 - (3-2)/12)}]`
    
    `= [13/4 ÷ { 5/4 - 1/2 (5/2 - 1/12)}]`
    
    `= [ 13/4 ÷ { 5/4 - 1/2 ((30 - 1)/12)}]`
    
    `= [ 13/4 ÷ { 5/4 - 29/24}]`
    
    `= [ 13/4 ÷ { (30 - 29)/24}]`
    
    `= [ 13/4 ÷ 1/24]`
    
    `= [ 13 xx 24]`
    
    `= 78`.

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  3. Question:If `617 ÷ 24.68 + x = 90`,find the value of `x`. 

    Answer
    Let, `617 ÷ 24.68 + x = 90`.
    
    Then,
    
    `617/24.68 + x = 90`
    
    or `25 + x = 90`
    
    or `x = (90 - 25)`
    
    `= 65`

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  4. Question:`1 +1/` `1 + 1/` `1 + 1/5` 

    Answer
    Given Expression ,
        `1 + 1/`
    
        `1 + 1/((6/5))`
    
        `= 1 + 1/`
    
        `= 1 +5/6`
    
        `= 1 + 1/(11/6)`
    
        `= (1 + 6)/(11)`
    
        `= 16/11`.

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  5. Question:`1 - 5/` `7 + 1` `4 + 1` `2 + 1/3` 

    Answer
    Given Expression ,
    
     `= 1 - 5/`
    
     `7 + 1/`
    
     `4 + 1/(7/3)`
    
     `= 1 - 5/`
        
     `7 + 1/4 + ( 3/7)`
    
     `= 1 - 5/`
        
     ` 7 + 1/(31/7)`
    
     `= 1 - 5/`
        
     
     `7 + 7/(31)`
    
     `= 1 - 5/(224/31)`
    
     `= (1 - (5 xx 31)/(224))`
    
     `= ((224 -155)/(224))`
    
     `= (69)/(224)`

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  6. Question:A boy was asked to multiplied a certain number by `53`.He multiplied it by `35` and got his answar less than the correct one by `1206`.Find the number to be multiplied 

    Answer
    Let the required number be x.Then,
    
    `53x -35x`
    
    `= 1206` or `18x`
    
    `= 1206` or `x = 67`
    
    :. Required number `= 67`.

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  7. Question:In a callege, `1/5`th of the girls and `1/8` th of the boys took part in a social comp. What of the total number of students in the college took part in the camp. 

    Answer
    Out of `5` girls `1` took in the camp.
    
    Out of `8` boys `1` took part in the camp.
    
    :. Out of `13` students ,`2` took part in the camp .
    
    :.`2/13` of the total strength took part in the camp .

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  8. Question:The highest score in an ining was `3/11` of the total and the next highest was `3/11` of the remainder . If the scores differed by `9`,find the total score. 

    Answer
    Let, total scores be x ,The highest scores .`(3x)/(11)`.
    
    Remainder `= (x - (3x)/(11))`
    
    `= (8x)/(11)`.
    
    Next highest 
    
    `= 3/11` of `(8x)/(11)`
    
    `= (24x)/(121)`.
    
    `:. (3x)/(11) - (24x)/(121) = 9`
    
    or `33x - 24x`
    
    `= 9 xx 121`.
    
    or `9x = 9 xx 121`
    
    or x `= 121`
    
    Hence total score`= 121`.

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  9. Question:In a km race, A beats B by 28 metres or 7 seconds. Find A'S time over the course. 

    Answer
    Clearly, B covers 28 m in 7 seconds.
    
    :.B,s time over the course` = (7/28 xx 1000)` sec = 250 seconds.
    
    :. A's time over the course = (250 - 7) sec = 243 sec.
    
       = 4 min. 3 sec.

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  10. Question:A runs` 1 3/4` times as fast as B. If A gives B a start of 84 m,how far must the winning post be so that A and B might reach it at the same time ? 

    Answer
    The ratio of the rates of A and B` = 7/4 : 1 = 7 : 4.`
    
    So, in a race of 7 m, A gains 3 m over B.
    
    :. 3m are gained by A in a race of 7m.
    
    :. 84 m are gained by A in a race of` (7/3 xx 84)` m = 196 m.
    
    :. Winning post must be 196 m away from the starting point.

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