Joshep and Kuntal work in a factory. Joshep takes 5 minutes less time than Kuntal to make a product. Joshep makes 6 product more than Kuntal while working for 6 hours. Calculate the number of products Kuntal makes during that time.

Explanation

Let Kuntal makes x products in 6 hours.
`:.` Joshep makes (x+6) products in 6 hours.
`:.` Kuntal makes 1 product in `(6)/(x)` hours `=(6)/(x)xx60" minutes "=(360)/(x)` minutes.
and Joshep makes 1 product in `(6)/(x+6)` hours
`(6)/(x+6)xx60` minutes.
`=(360)/(x+6)` minutes.
As per questions, `(360)/(x)-(360)/(x+6)=5`
or, `360((1)/(x)-(1)/(x+6))=5or,72((1)/(x)-(1)/(x+6))=1`
or, `(x+6-x)/(x(x+6))=(1)/(72)or,(6)/(x^(2)+6x)=(1)/(72)`
or, `x^(2)+6x=432`
or, `x^(2)+6x-432=0...............(1)`
Comparing (1) with `ax^(2)+bx+c=0,(ane0)`, we get, `a=1,b=6andc=-432`
`:.` by Sreedhar Acherya's formula we get, `x=(-6pmsqrt((6)^(2)-4xx1xx(-432)))/(2xx1)`
or, `x=(-6pmsqrt(36+1728))/(2)`
or, `x=(-6pmsqrt1764)/(2)or,x=(-6pm42)/(2)`
`:.x=(-6+42)/(2)` (taking +sign) and`:.x=(-6-42)/(2)` (taking -sign)
`=(36)/(2)andx=(-48)/(2)`
`=18andx=-24`
But the number of products can not be negative. `:.x=18`.
Hence Kuntal makes 18 products in 6 hours.