If the velocity of the stream is 2 km/hr, then the time taken by Ratanmajhi to cover 21 km in downstream and upstream is 10 hours.Hence find the required quadratic equation.

Explanation

Let the velocity of the boat of Ratanmajhi =x km/hr.
`:.` Velocity of the boat in downstream =(x+2) km/hr and in the upstream =(x-2) km/hr.
`:.` to reach 21 km in downstream, the time required `=(21)/(x+2)` hours
and to come back, the time required `=(21)/(x-2)` hours
As per question, `(21)/(x+2)+(21)/(x-2)=10`
or, `21((1)/(x+2)+(1)/(x-2))=10`
or, `21{(x-2+x+2)/((x+2)(x-2))}=10`
or, `21{(2x)/(x^(2)-2^(2))}=10`
or, `(42x)/(x^(2)-4)=10or,(21x)/(x^(2)-4)=5or,5x^(2)-20=21x`
or, `5x^(2)-21x-20=0`
Hence the required quadratic equation is `5x^(2)-21x-20=0`.