(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.

 ncert cbse 10th mathematics chapter 3 exercise3.6 pair of linear equations in two variables

2

 (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.

let x = number of days for a woman alone to finish the work

and y = number of days for a man alone to finish the work

 

This is a problem on time and work so remember to take reciprocals of x , y and time

 

2 women and 5 men can together finish an embroidery work in 4 days

so

[2/x] +[5/y]=[1/4]

3 women and 6 men can finish it in 3 days

so

[3/x]+[6/y] =[1/3]

equations are

[2/x] +[5/y]=[1/4]

[3/x]+[6/y] =[1/3]

to get rid of (1/x) and (1/y)

use a=(1/x) and b=(1/y)

 

equations change to 

2a+5b= [1/4]      *3

3a+6b= [1/3]      *2

-------------------------------------eliminate a

6a +15b=[3/4]

6a+12b=[2/3]

------------------------------------subtracting

     3b =[3/4] -[2/3]

     3b =[1/12]    

      

 b=[1/36]

 

substitute in 3a+6b= [1/3]

3a +6*(1/36) =[1/3]

3a = [1/3] - [1/6]

3a = [1/6]

 

a=[1/18]

a=[1/18] ,b=[1/36]

take reciprocal

x =18 days  , y = 36 days

 

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. 

Let x = speed of her rowing in still water in km/hr

and y = speed of the current in km/hr

speed downstream = (x+y)

speed upstream = (x-y)

time = distance / speed

 

downstream 20 km in 2 hours

means 

2 =20/(x+y) 

or 

x+y = 20/2

x+y =10-------------------(1)

 

upstream 4 km in 2 hours

means

2 =4/(x-y) 

or

x-y =4/2

x-y =2----------------------(2)

x+y =10-------------------(1)

x-y =2----------------------(2)

------------------------------------------adding

2x = 12

 

x= 6km/hr

 

substitute in x-y =2

to get

y=4km/hr

 

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ncert cbse 10th mathematics chapter 3 optional exercise 3.7 

 The ages of two friends Ani and Biju differ by 3 years. Ani’s father  is twice as old as Ani and Biju is twice as old as his sister Cathy. The ages of Cathy and Ani’s father differ by 30 years. Find the ages of Ani and Biju

solution

 

2. One says, “Give me a hundred, friend! I shall then become twice as rich as you”. The other replies, “If you give me ten, I shall be six times as rich as you”. Tell me what is the amount of their (respective) capital? 

solution

3. A train covered a certain distance at a uniform speed. If the train would have been 10 km/h faster, it would have taken 2 hours less than the scheduled time. And, if the train were slower by 10 km/h; it would have taken 3 hours more than the scheduled time. Find the distance covered by the train. 

solution  

 

4. The students of a class are made to stand in rows. If 3 students are extra in a row, there would be 1 row less. If 3 students are less in a row, there would be 2 rows more. Find the number of students in the class.

solution  

5. In a ∆ ABC, ∠ C = 3 ∠ B = 2 (∠ A + ∠ B). Find the three angles.

solution

 

Solve the following pair of linear equations:

 px + qy = p – q 

 qx – py = p + q

solution

 

(ii) ax + by = c
     bx + ay = 1 + c

solution  

 

(iii) 

(x/a) -(y/b) = 0

ax +by = (a^2)  + (b^2)

solution  

 

(iv)

(a – b)x + (a + b) y = (a^2) – 2ab – (b^2)

(a + b)(x + y) = (a^2) + (b^2 )

solution

 

(v)

152x – 378y = – 74

–378x + 152y = – 604

solution   

 ABCD is a cyclic quadrilateral  Find the angles of the cyclic quadrilateral,

if angles are A =(4y+20) , B =(3y-5) , C=(-4x), D=(-7x+5)

solution

 

exercise 3.6

2

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. 

solution

 

 (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.

solution

 

(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

 

 

 
 
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