CBSE Class 10 Sample Paper for 2021 Boards - Maths Standard

Question 36 - CBSE Class 10 Sample Paper for 2021 Boards - Maths Standard

Last updated at Oct. 27, 2020 by Teachoo

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.

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

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 – 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
(𝐷𝑖𝑠𝑡𝑎𝑛𝑐𝑒 𝑜𝑓 16 𝑘𝑚)/(𝑆𝑝𝑒𝑒𝑑 𝑢𝑝𝑠𝑡𝑟𝑒𝑎𝑚) + (𝐷𝑖𝑠𝑡𝑎𝑛𝑐𝑒 𝑜𝑓 24 𝑘𝑚)/(𝑆𝑝𝑒𝑒𝑑 𝑑𝑜𝑤𝑛𝑠𝑡𝑟𝑒𝑎𝑚) = 6
𝟏𝟔/(𝒙 − 𝒚) + 𝟐𝟒/(𝒙 + 𝒚) = 6
We know that,
Speed = (𝐷𝑖𝑠𝑡𝑎𝑛𝑐𝑒 )/𝑇𝑖𝑚𝑒
Time = (𝐷𝑖𝑠𝑡𝑎𝑛𝑐𝑒 )/𝑆𝑝𝑒𝑒𝑑
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
(𝐷𝑖𝑠𝑡𝑎𝑛𝑐𝑒 𝑜𝑓 12 𝑘𝑚)/(𝑆𝑝𝑒𝑒𝑑 𝑢𝑝𝑠𝑡𝑟𝑒𝑎𝑚) + (𝐷𝑖𝑠𝑡𝑎𝑛𝑐𝑒 𝑜𝑓 36 𝑘𝑚)/(𝑆𝑝𝑒𝑒𝑑 𝑑𝑜𝑤𝑛𝑠𝑡𝑟𝑒𝑎𝑚) = 6
𝟏𝟐/(𝒙 − 𝒚) + 𝟑𝟔/(𝒙 + 𝒚) = 6
We know that,
Speed = (𝐷𝑖𝑠𝑡𝑎𝑛𝑐𝑒 )/𝑇𝑖𝑚𝑒
Time = (𝐷𝑖𝑠𝑡𝑎𝑛𝑐𝑒 )/𝑆𝑝𝑒𝑒𝑑
Our equations are
16(1/(𝑥 − 𝑦))+24(1/(𝑥 + 𝑦))=6 …(1)
12(1/(𝑥 − 𝑦))+36(1/(𝑥 + 𝑦))=6 …(2)
So, our equations become
Solving
16u + 24v = 6 …(3)
12u + 36v = 6 …(4)
Let 1/(𝑥 − 𝑦) = u
1/(𝑥 + 𝑦) = v
12u + 36v = 6
From (3)
16u + 24v = 6
16u = 6 – 24v
u = (6 − 24𝑣)/16
Putting value of u in (4)
12u + 36v = 6
12((6 − 24𝑣)/16)+36𝑣=6
3((6 − 24𝑣)/4)+36𝑣=6
Multiplying both sides by 4
4 × 3((6 − 24𝑣)/4)+"4 ×" 36𝑣="4 ×" 6
3(6 – 24v) + 144𝑣= 24
18 – 72v + 144v = 24
– 72v + 144v = 24 – 18
72v = 6
v = 𝟔/𝟕𝟐
v = 𝟏/𝟏𝟐
Putting v = 1/12 in equation (3)
12u + 36v = 6
12u + 36(1/12) = 6
12u + 3 = 6
12u = 6 − 3
12u = 3
u = 3/12
u = 𝟏/𝟒
So, u = 1/4 & v = 1/12
But we need to find x & y
We know that
u = 𝟏/(𝒙 − 𝒚)
1/4 = 1/(𝑥 − 𝑦)
x – y = 4
v = 𝟏/(𝒙 + 𝒚)
1/12 = 1/(𝑥 + 𝑦)
x + y = 12
So, our equations become
x – y = 4 …(6)
x + y = 12 …(7)
Adding (6) and (7)
(x – 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 – 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 – 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

CBSE Class 10 Sample Paper for 2021 Boards - Maths Standard

Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 10 years. He provides courses for Maths and Science at Teachoo.