MathematicsRani decided to distribute some amount to poor students for their books. If there are 8 students less, everyone will get Rs. 10 more. If there are 16 students more, everyone will get Rs. 10 less. What is the number of students and how much does each get? Also, find the total amount distributed?

Rani decided to distribute some amount to poor students for their books. If there are 8 students less, everyone will get Rs. 10 more. If there are 16 students more, everyone will get Rs. 10 less. What is the number of students and how much does each get? Also, find the total amount distributed?


  1. A
    No. of students- 32, Amount per student- Rs. 30, Total amount- Rs. 960
  2. B
    No. of students- 60, Amount per student- Rs. 40, Total amount- Rs. 800
  3. C
    No. of students- 72, Amount per student- Rs. 50, Total amount- Rs. 670
  4. D
    No. of students- 22, Amount per student- Rs. 20, Total amount- Rs. 360 

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    Solution:

    Given that if the count of students is 8 less then everyone will get Rs. 10 more and if the count of students is 16 more then everyone gets Rs. 10 less.
    Let the amount given to one person be Rs. x.
    Let the number of students be y.
    So,
    Total amount to be distributed = yx.
    Now, according to the first condition,
    (y-8)(+ 10) = yx
    According to the second condition,
    (+ 16) (- 10) =yx
    Therefore, we can say that,
    (y-8)(x+10) = (y+16)(x-10)
    Simplifying the above equation,
    yx -8+10-80 = yx + 16-10-160
    yx -yx +160 -80 = 16+8-10y-10y
    80 = 24-20(1)
    Also, since the total amount to be distributed is xy in both the case,
    yx = (y-8)(x+ 10)
    yx = yx -8x+10-80
    yx - yx +80 = 10y- 8x
    80 = 10- 8(2)
    Equating the RHS values from equation 1 and 2,
    10- 8= 24- 20 y
    10+ 20= 24+ 8x
    30= 32 x
    y = 3230x………….(3)
    Putting values of equation 3 in equation 1,
    80 = 24x - 20(3230x)
    80 = 24 x - 643x
    80 = 83 x
    x=30……..(4)
    Putting the values of equation 4 to equation 3,
    y = 32 × 3030
    y = 32
    Therefore, the number of students is y = 32 and the amount per student is x = Rs. 30.
    Thus, the total amount will be 32 × 30 = Rs. 960.
    Hence, option (1) is correct.
     
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