MathematicsA man wished to give ₹12 to each person and found that he fell short of ₹6 when he wanted to give to all the persons present. He, therefore, distributed ₹9 to each person and found that ₹9 were left over. How much money did he have and how many people were there?

A man wished to give ₹12 to each person and found that he fell short of ₹6 when he wanted to give to all the persons present. He, therefore, distributed ₹9 to each person and found that ₹9 were left over. How much money did he have and how many people were there?


  1. A
    ₹12, 4 people
  2. B
    ₹5, 4 people
  3. C
    ₹52, 5 people
  4. D
    ₹54, 5 people 

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    Solution:

    Given that, a man fell short of ₹6 when he wanted to give all present ₹12 each.
    Let the number of persons be x and the amount of money he had y.
    So,
    12x-6=y…………….(1)
    He distributed ₹9 to each person and found that ₹9 were left over.
    Therefore, 9x+9=y…………..(2)
    Solve equations (1) and (2) to determine the amount of money he had and the number of persons.
    From (1) and (2),
    ⇒12x-6=9x+9 ⇒3x=15 ⇒x=5 Substitute x=5 in equation (2),
    ⇒y=9x+9 ⇒y=9(5)+9 ⇒y=45+9 ⇒y=54 Thus, there were 5 persons and he had ₹54.
    Therefore, the correct option is 4.
     
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