A group of students decided to buy an. F.M. Radio (transistor) from 256 to 300 rupees. But at the last moment two students backed out of the decision so that the remaining students had to pay one rupee each more than they had planned. What was the price of F.M. Radio, if the students paid equal shares?
Let the cost of F.M. Radio =RS.x
and the total number of students =n
`because` Share of each student `=RS.(x)/(n)`
But, if 2 students backed out of the decision, then share of each student `=RS.(x)/(n-2)`
`because` But the given condition,
`(x)/(n-2)-(x)/(n)=1impliesx((1)/(n-2)-(1)/(n))=1`
`=x((n-n+2)/(n(n-2)))=1impliesx=(n^(2)-2n)/(2)” “……(1)`
But, `265lexle300″ “(“given”)`
`implies265le(n^(2)-2n)/(2)le300″ “[“from”(1)]`
`implies530len^(2)-2n+1le601″ “(“multiplying both sides by 2”)`
`implies531len^(2)-2n+1le601″ “(“adding 1 to each side”)`
`implies531le(n-1)^(2)le601`
`impliessqrt531len-1lesqrt601`
`implies1+sqrt531lenle1+sqrt601`
If `nle1+sqrt531impliesnle1+23.04….impliesnle24.04″ “……(2)`
If `nle1+sqrt601impliesnle1+24.515…..impliesnle25.52……(3)`
From (2) and (3), we get
`n=25″ “(because”number of students cannot be in fraction”)`
`because` From (1), we get
`x=((25)^(2)-2xx25)/(2)=(625-50)/(2)=(575)/(2)=RS.287.500`