NCERT Class 10 Mathematics

66 MATHEMATICS

Let t 2 be the time, in hours, taken by the boat to go 44 km downstream. Then

2

t^44.

x y

✁

The total time taken, t 1 + t 2 , is 10 hours. Therefore, we get the equation

30 44

x yxy

✁

✂ ✁

= 10 (1)

In the second case, in 13 hours it can go 40 km upstream and 55 km downstream. We
get the equation

40 55

x yxy

✁

✂ ✁

= 13 (2)

Put

(^11) uvand
xy xy

✂ ✁ (3)

On substituting these values in Equations (1) and (2), we get the pair of linear
equations:

30 u + 44v =10or30u + 44v – 10 = 0 (4)

40 u + 55v =13or40u + 55v – 13 = 0 (5)

Using Cross - multiplication method, we get

44 ( 13) 55( 10)

u

✂ ✂ ✂

=

1

40 ( 10) 30 ( 13) 30 (55) 44(40)

v



✂ ✂ ✂ ✂

i.e.,
22

u

✄

=

1

10 110

v

☎

✄ ✄

i.e., u =

(^1) ,
5
v =

1

11

Now put these values of u and v in Equations (3), we get

11

xy 5

✂

and

11

xy 11

✁

i.e., x – y = 5 andx + y = 11 (6)

Adding these equations, we get
2 x =16

i.e., x =8

Subtracting the equations in (6), we get

2 y =6

i.e., y =3