CBSE Class 10 Sample Paper for 2021 Boards - Maths Standard

Class 10
Solutions of Sample Papers for Class 10 Boards

## A motorboat covers a distance of 16km upstream and 24km downstream in 6 hours. In the same time it covers a distance of 12 km upstream and 36km downstream. Find the speed of the boat in still water and that of the stream.

Β

This video is only available for Teachoo black users

Β

Note : This is similar to Example 19 ,Β  Chapter 3 Class 10 Pair of Linear Equations in 2 Variables (NCERT Book)

Introducing your new favourite teacher - Teachoo Black, at only βΉ83 per month

### Transcript

Question 36 A motorboat covers a distance of 16km upstream and 24km downstream in 6 hours. In the same time it covers a distance of 12 km upstream and 36km downstream. Find the speed of the boat in still water and that of the stream.Let the Speed of Boat in still water be x km/hr & let the Speed of Stream be y km/hr Now, Speed Downstream = x + y Speed Upstream = x β y Given that A boat goes 16 km upstream and 24 km downstream in 6 hours Time taken to go 16 km upstream + Time taken to go 24 km downstream (π·ππ π‘ππππ ππ 16 ππ)/(πππππ π’ππ π‘ππππ) + (π·ππ π‘ππππ ππ 24 ππ)/(πππππ πππ€ππ π‘ππππ) = 6 ππ/(π β π) + ππ/(π + π) = 6 We know that, Speed = (π·ππ π‘ππππ )/ππππ Time = (π·ππ π‘ππππ )/πππππ Similarly, A boat goes 12 km upstream and 36 km downstream in 6 hours Time taken to go 12 km upstream + Time taken to go 36 km downstream (π·ππ π‘ππππ ππ 12 ππ)/(πππππ π’ππ π‘ππππ) + (π·ππ π‘ππππ ππ 36 ππ)/(πππππ πππ€ππ π‘ππππ) = 6 ππ/(π β π) + ππ/(π + π) = 6 We know that, Speed = (π·ππ π‘ππππ )/ππππ Time = (π·ππ π‘ππππ )/πππππ Our equations are 16(1/(π₯ β π¦))+24(1/(π₯ + π¦))=6 β¦(1) 12(1/(π₯ β π¦))+36(1/(π₯ + π¦))=6 β¦(2) So, our equations become Solving 16u + 24v = 6 β¦(3) 12u + 36v = 6 β¦(4) Let 1/(π₯ β π¦) = u 1/(π₯ + π¦) = v 12u + 36v = 6 From (3) 16u + 24v = 6 16u = 6 β 24v u = (6 β 24π£)/16 Putting value of u in (4) 12u + 36v = 6 12((6 β 24π£)/16)+36π£=6 3((6 β 24π£)/4)+36π£=6 Multiplying both sides by 4 4 Γ 3((6 β 24π£)/4)+"4 Γ" 36π£="4 Γ" 6 3(6 β 24v) + 144π£= 24 18 β 72v + 144v = 24 β 72v + 144v = 24 β 18 72v = 6 v = π/ππ v = π/ππ Putting v = 1/12 in equation (3) 12u + 36v = 6 12u + 36(1/12) = 6 12u + 3 = 6 12u = 6 β 3 12u = 3 u = 3/12 u = π/π So, u = 1/4 & v = 1/12 But we need to find x & y We know that u = π/(π β π) 1/4 = 1/(π₯ β π¦) x β y = 4 v = π/(π + π) 1/12 = 1/(π₯ + π¦) x + y = 12 So, our equations become x β y = 4 β¦(6) x + y = 12 β¦(7) Adding (6) and (7) (x β y) + (x + y) = 4 + 12 2x = 16 x = 16/2 x = 8 Putting x = 8 in (7) x + y = 12 8 + y = 12 y = 12 β 8 y = 4 So, x = 8, y = 4 is the solution of the given equation Hence Speed of boat in still water = x = 8 km/hr Speed of stream = y = 4 km/hr y = 12 β 8 y = 4 So, x = 8, y = 4 is the solution of the given equation Hence Speed of boat in still water = x = 8 km/hr Speed of stream = y = 4 km/hr