Dear Reader, below are practice questions dealing with contributions / sharing by members in a group.

Question 1

A few students of Ramiah Engineering College went for a party in the nearby hotel to celebrate the success of their College Cricket Team in a recent match. The total bill amount was Rs.3200. The leader of the group found that two students had not brought any amount with them. The two people requested others to share the bill and assured them that they will pay afterwards. This resulted in each of the members paying Rs.80 more. How many students went for the party?

a) 10 b) 12 c) 16 d) none of these.

Answer : a) 10

Solution :

Let 'x' be the number of persons in the group and let 'y' be amount per head which they have to pay.
Then xy = 3200.
or y = 3200/x
Since two friends have forget the purse, x-2 persons should share the total amount (3200).
If they share, they have to make an extra contribution of Rs.80 to pay up the bill

That is x-2 persons should pay y+80 each
or (x-2)(y+80) = 3200
or y+80 = 3200/(x-2)
or y = 3200/(x-2) - 80
Therefore we have got two equations namely, 
y= 3200/x and y = 3200/(x-2) - 80

Comparing these two, we get
3200/x = 3200/(x-2) - 80
Solving this we get
x² - 2x -80 = 0
or (x-10) (x+8) = 0
or x = 10 or x = -8
Since 'x' denotes the number of persons, it should be positive.
So, x =10

Question 2

Surya Elementary School arranged for a picnic for its 124 students. Since 24 students could not contribute for their picnic other students had to pay Rs.19.20 more than what they would have contributed if all of them had brought money. Find out the amount that all would have been paid in case all the students had contributed?

a) 100 b) 80 c) 60 d) 120

Answer : b) 80

Solution :

Let x be the amount that would have been paid by each student if all of them contribute.
Therefore, Total amount = 124x ...(1)
But, only 100 students paid. (24 could not pay). These 100 students paid Rs. 19.20 more than the planned share.
Therefore, Amount paid by 100 students = 100 (x + 19.20) ...(2)
But, the amount paid by 100 students should match the originally planned amount of 124x.

Equating the values of 1 and 2.
124x = 100 (x + 19.20)
124x = 100 x + 1920
24 x = 1920
x = 80

Question 3

A group of teachers from Venkat Engineering College went to a hotel for celebrating a happy event with an understanding all of them will share the expenses. The bill amount was Rs.2560. Since four teachers did not bring their purse other teachers had to contribute Rs.32 more. How many teachers contributed towards the bill settlement?

a) 24 b) 16 c) 20 d) none of these.

Answer : b) 16

Solution :

Let the number of teachers be x.
Total bill amount = Rs. 2560.
Share of each teacher = 2560/x
But, 4 teachers failed to bring their purse.
Number of teachers who actually paid = x - 4
Each one had paid Rs. 32 more than the planned share of 2560/x so as to settle the bill amount of Rs. 2560
Therefore, (x- 4)(2560/x + 32) = 2560
2560 + 32x - 10240/x - 128 = 2560
Multiply both sides by x.

2560x + 32x² - 10240 - 128x=2560x
32x² - 128x - 10240=0
x² - 4x - 320=0
Factorizing the above equation, we get
(x - 20)(x + 16) = 0
x = +20 or -16

Since x cannot be negative, x = 20 = total number of teachers.
Since, 4 teachers did not carry their purses, number present at the party = 20 - 4 = 16
Therefore, our answer = 16.