SOLVING LINEAR EQUATIONS WORD PROBLEMS

About "Solving Linear Equations Word Problems"

Solving Linear Equations Word Problems :

Here we are going to see some example problems on solving equations.

Solving Linear Equations Word Problems - Practice questions

Question 4 :

On selling a T.V. at 5% gain and a fridge at 10% gain, a shopkeeper gains ₹2000. But if he sells the T.V. at 10% gain and the fridge at 5% loss, he gains Rs.1500 on the transaction. Find the actual price of the T.V. and the fridge. 

Solution :

5x/100 +  10y/100 = 2000

x/20 + y/10 = 2000/1

Taking the L.C.M. of the denominator and then solving it, we get.

(x + 2y)/20 = 2000 

x + 2y = 40000  ...........................(1)

10x/100 - 5y/100 = 1500

x/10 - y/20 = 1500/1

Taking the L.C.M. of the denominator and then solving it, we get.

(2x - y)/20 = 1500

2x - y = 30000  ........................(2)

(1) + 2(2) 

               x + 2y = 40000

              4x  - 2y  = 60000 

             ------------------

              5x  =  100000

               x  =  100000/5  =  20000

By applying the value of x in (1), we get

20000 + 2y = 40000

 2 y  =  40000 - 20000

 2y  =  20000

  y  =  10000

Question 5 :

Two numbers are in the ratio 5 : 6. If 8 is subtracted from each of the numbers, the ratio becomes 4 : 5. Find the numbers.

Solution :

Let the two no be x and y

So,  x / y = 5 / 6

6 x = 5 y

6 x - 5 y = 0  ----(1)

(x - 8)/(y - 8) = 4 / 5

5(x - 8)  =  4(y - 8)

5 x - 40  =  4y - 32

5x - 4y  =  -32 + 40

5x - 4y  =  8 ----(2)

(1) x 4 ==>  24x - 20y  =  0

(2) x 5==> 25x - 20y  =  40

              (-)   (+)         (-)

              --------------------

              -x   =  -40

             x  =  40

By applying the value of x in (1), we get 

 6(40)  =  5y

5y  =  240

  y  =  48

Hence the required numbers are 40 and 48.

Question 6 :

4 Indians and 4 Chinese can do a piece of work in 3 days. While 2 Indians and 5 Chinese can finish it in 4 days. How long would it take for 1 Indian to do it? How long would it take for 1 Chinese to do it?

Solution :

Let x and y be the number of days taken by each indian and each chinese.

1/x  =  work done 1 Indian in 1 day

1/y  =  work done by 1 Chinese in 1 day

4/x + 4/y  =  1/3

2/x + 5/y  =  1/4

Let 1/x  =  a and 1/y = b

4a + 4b  - 1/3  =  0

2a + 5b - 1/4  =  0   

a/(-1 + (5/3))  =  b/((-2/3) + 1)  =  1/(20 - 8)

a/(2/3))  =  b/(1/3)  =  1/12

a  =  1/18, b =  1/36

x  =  18 and y  =  36

Hence the Indians are taking 18 days to complete the work and Chinese are taking 36 days to complete the work.

After having gone through the stuff given above, we hope that the students would have understood, "Solving Linear Equations Word Problems" 

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