Question

7. A group of friends goes for dinner and gets
bill of Rs 2400. Two of them says that they
have forgotten their purse so remaining make
an extra contribution of Rs 100 to pay up the
bill. Tell the no. of person in that group.
(a) 8 persons
(b) 7 persons
(c)12 persons
(d)None of these

Answer 1

Explanation:

Let 'x' be the number of perons in the group and let 'y' be

amount per head which they have to pay.

Then xy = 2400.

or y = 2400/x

Since two friends have forget the purse, x-2 persons should

share the total amount(2400).

If they share, they have to make an extra contribution of

100 Rs to pay up the bill

That is x-2 persons should pay y+100 each

or (x-2)(y+100) = 2400

or y+100 = 2400/(x-2)

or y = 2400/(x-2) - 100

Therefore we have got two equations namely,

y= 2400/x and y = 2400/(x-2) - 100

Comparing these two, we get

2400/x = 2400/(x-2) - 100

Solving this we get

x^2 - 2x -48 = 0

or (x-8) (x+6) = 0

or x = 8 or x = -6

Since 'x' denotes the number of persons, it should be positive.

So, x = 8.

Answer 2

Given,

A group of friends have gone for dinner and get a

bill of Rs 2400.

Two of them forgot their purse so the remaining friends made an extra contribution of Rs 100 to pay up the bill.

To find,

The number of persons in the group.

Solution,

We can simply solve this mathematical problem using the following process:

Let us assume that the number of persons in the group is x.

The bill amount of each individual

= Total bill amount / total number of persons in the group

= Rs 2400/x

Now, according to the question;

Total bill amount of the two individuals who have left their purse = total number of individuals who paid the money x extra payment by each such individual

=> 2(Rs 2400/x) = 100(x-2)

=> 4800/x = 100x - 200

=> 100x^2 - 200x = 4800

=> x^2 - 2x - 48 = 0

=> x^2 - 8x + 6x - 48 = 0

=> x(x-8) + 6(x-8) = 0

=> (x-8)(x+6)=0

=> x = 8 or x = -6

However, the number of individuals can't be negative.

Hence, there is a total of 8 people in the group.