20 children were sharing equally to the cost of a present for their teacher when 4 of the children decided not to contibute each children had pay 1.50

Question

how much did the present cost sir give in short method

Answer 1

Hi Habeeba, 

 

This is how you would solve this problem. 

 

Let "c" be the cost of the present

 

When 20 students were splitting the cost of the present, lets say each student payed "a"

 

When 4 students backed out, 16 students had to split the total cost of the present. And when they did, each student had to pay "a + 1.5"

 

Hence,

 

Cost of present = (number of students) × amount paid by each student

 

When 20 students were paying,

 

c = 20 × a    ----> Equation 1

 

When 16 students are paying,

 

c = 16 × (a + 1.5)    -----> Equation 2

 

To get the value of "c" substitute the value of "a" from Equation 1 in Equation 2

 

c = 16 × ((c/20) + 1.5)

 

c = ((16×c)/20) + (1.5 × 16)

 

c = (4×c)/5 + 24

 

Bring all the "c" terms together

 

((5-4)×c)/(5) = 24

 

⇒ Cost of present = 24 × 5 = 120

 

Answer: Cost of present = 120