MathematicsThe expenses of a lunch are partly constant and partly proportional to the number of guests. The expenses amount to  ₹65 for 7guests and ₹97 for 11 guests. How much do the expenses for 18 guests amount to?

The expenses of a lunch are partly constant and partly proportional to the number of guests. The expenses amount to  ₹65 for 7guests and ₹97 for 11 guests. How much do the expenses for 18 guests amount to?


  1. A
    100
  2. B
    153
  3. C
    120
  4. D
    140 

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    Solution:

    Given that, the expenses of a lunch are partly constant and partly proportional to the number of guests.
    Let the expense for one guest be x and fixed expense be y.
    As the expenses amount to ₹65 for 7 guests,
    7x+y=65…………..(1)
    As the expenses amount to ₹97 for 11 guests,
    11x+y=97 …………..(2)
    Subtracting equation (1) from (2), we get,
    ⇒11x+y-7x-y=97-65 ⇒4x=32 ⇒x=8 Substituting x=8 in equation (1),
    ⇒7(8)+y=65 ⇒56+y=65 ⇒y=9 Now, for 18 guests,
    Total expense = 18x+y
    ⇒y=188+9 ⇒y=153 So, the expense for 18 guests is ₹153.
    Hence, option 2 is correct.
     
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