# CBSE 2016 Board Paper

10th standard Math - Q31. Quadratic Equations

#### Video Explanation

Speed of motorboat in still water = 24 km/hr
Let speed of stream be x km/hr
Upstream speed of boat = (24 – x)km/hr
Time taken to travel 32 km upstream = $$frac{32}{24 - x}$hr Downstream speed of boat =$24 + x) km/hr
Time taken to travel 32 km downstream = $$frac{32}{24 + x}$ The boat takes an hour longer to travel upstream than to travel downstream i.e., $\frac{32}{24 - x}$ = $\frac{32}{24+x}$ + 1 $\frac{32}{24 - x}$ = $\frac{32 + 24 + x}{24 + x}$ $\frac{32}{24 - x}$ = $\frac{56 + x}{24 + x}$ Cross multiply and solve for x 32$24 + x) = (24 – x)(56 + x)
32 × 24 + 32x = 24 × 56 + 24x - 56x - x2
32 × 24 + 32x = 56 × 24 – 32x - x2
x2 + 64x + 24 (32 - 56) = 0
x2 + 64x - 24 × 24 = 0
x2 + 72x – 8x – 576 = 0
{x + 72) (x - 8) = 0
x = - 72 or x = 8
Speed of stream cannot be negative.
So, speed of stream = 8 km/hr