# Gujarat Board Solutions Class 10 Maths Chapter 3 Pair of Linear Equations in Two Variables Ex 3.6

Gujarat Board Solutions Class 10 Maths Chapter 3 Pair of Linear Equations in Two Variables Ex 3.6

## Gujarat Board Textbook Solutions Class 10 Maths Chapter 3 Pair of Linear Equations in Two Variables Ex 3.6

Question 1.

Solve the following pairs of equations by reducing them to a pair of linear equations:

Hence, the solution of the given pair of

equations is x = 4, y = 5.

Verification: Substituting x = 4, y = 5, we

find that both the equations (1) and (2) are

satisfied as shown below:

Hence, the solution is correct.

(v) The given pair of equations is

Then the equations (3) and (4) can be rewritten as

7υ – 2u = 5

8υ + 7u = 15

7υ – 2u – 5 = 0

8υ + 7u – 15 = 0

To solve the equations by the cross multiplication method, we draw the diagram below:

(vi) The given pair of equations is

6x + 3y = 6xy

2x + 4y = 5xy

(Dividing throughout by xy)

Then equations (1) and (2) can be rewritten as

6υ + 3u = 6

2υ + 4u = 5

Multiplying equation (6) by 3, we get

6υ + 12u = 15

Subtracting equation (5) from equation (7), we get

Question 2.

Formulate the following problems as a pair of equations, and hence find their solutions:

(i) Ritu can row downstream 20 km in 2 hours, and upstream 4 km in 2 hours. Find her speed of rowing in still water and the speed of the current.

(ii) 2 women and 5 men can together finish an embroidery work in 4 days, while 3 women and 6 men can finish it in 3 days. Find the time taken by 1 woman alone to finish the work, and also that taken by 1 man alone.

(iii) Roohi travels 300 km to her home partly by train and partly by bus. She takes 4 hours if she travels 60 km by train and the remaining by bus. If she travels 100 km by train and the remaining by bus, she takes 10 minutes longer. Find the speed of the train and the bus separately.

Solution:

(i) Let her speed of rowing in still water be x kim/hour and the speed of the current be y km/hour.

Then, her speed of rowing downstream

= (x + y) km/hour

and, her speed of rowing upstream

= (x – y) km/hour

Substituting this value of x in equation (1), we get

6 + y = 10

y = 10 – 6 = 4

Hence, the speed of her rowing in still water

is 6 km/hour and the speed of the current is 4 km/hour.

Verification: Substituting x = 6, y = 4, we

find that both the equations (1) and (2) are

satisfied as shown below:

x + y = 6 + 4 = 10

x – y = 6 – 4 = 2

Hence, the solution is correct.

(ii) Let the time taken by 1 woman alone to finish the embroidery work be x days and the time taken by 1 man alone to finish the embroidery be y days.

Hence, the time taken by 1 woman alone to finish the embroidery work is 18 days and the time taken by 1 man alone to finish the embroidery work is 36 days.

Verification : Substituting x = 18, y = 36,

we find that both the equations (1) and (2) are satisfied as shown below:

(iii) Let the speed of the train and the bus be x km/hour and y km/hour respectively.

When she travels 60 km by train and the remaining (300 – 60) km, i.e., 240 km by bus, the time taken is 4 hours.

So, the solution of the equations (1) and (2)

is x = 60 and y = 80.

Hence, the speed of the train is 60 km/hour and the speed of the bus is 80 km/hour.

Verification: Substituting x= 60, y = 80,

we find that both the equations (1) and (2) are satisfied as shown below:

Hence, the solution is correct.

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