# NCERT solution class 10 chapter 3 Pair of Linear Equations in Two Variables exercise 3.6 mathematics

## EXERCISE 3.6

#### Question 1:

Solve the following pairs of equations by reducing them to a pair of linear equations:         Let and , then the equations change as follows. Using cross-multiplication method, we obtain   Putting and in the given equations, we obtain Multiplying equation (1) by 3, we obtain

6p + 9q = 6 (3)

Adding equation (2) and (3), we obtain Putting in equation (1), we obtain  Hence,  Substituting in the given equations, we obtain By cross-multiplication, we obtain  Putting and in the given equation, we obtain Multiplying equation (1) by 3, we obtain Adding (2) an (3), we obtain Putting this value in equation (1), we obtain  Putting and in the given equation, we obtain By cross-multiplication method, we obtain  Putting and in these equations, we obtain By cross-multiplication method, we obtain Hence, x = 1, y = 2 Putting and in the given equations, we obtain Using cross-multiplication method, we obtain  Adding equation (3) and (4), we obtain Substituting in equation (3), we obtain

y = 2

Hence, x = 3, y = 2 Putting in these equations, we obtain Adding (1) and (2), we obtain Substituting in (2), we obtain Adding equations (3) and (4), we obtain Substituting in (3), we obtain Hence, x = 1, y = 1

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#### 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 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.

(i)Let the speed of Ritu in still water and the speed of stream be x km/h

and y km/h respectively.

Speed of Ritu while rowing

Upstream = km/h

Downstream = km/h

According to question, Adding equation (1) and (2), we obtain Putting this in equation (1), we obtain

y = 4

Hence, Ritu’s speed in still water is 6 km/h and the speed of the current is 4 km/h.

(ii)Let the number of days taken by a woman and a man be and y respectively.

Therefore, work done by a woman in 1 day = Work done by a man in 1 day = According to the question, Putting in these equations, we obtain By cross-multiplication, we obtain  Hence, number of days taken by a woman = 18

Number of days taken by a man = 36

(iii) Let the speed of train and bus be u km/h and v km/h respectively.

According to the given information, Putting and in these equations, we obtain Multiplying equation (3) by 10, we obtain Subtracting equation (4) from (5), we obtain Substituting in equation (3), we obtain Hence, speed of train = 60 km/h

Speed of bus = 80 km/h

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