CLASS-9SIMULTANEOUS LINEAR EQUATION - PROBLEM ON MISCELLANEOUS

MISCELLANEOUS PROBLEMS

Example.1) A jeweler has bars of 18 carat gold and 6 carat gold. How much of each must be melted together to obtained a bar of 12 carat gold weighing 160 gm ? it is given that pure gold is 24 carat.

18

Ans.) Percentage of gold in 18 carat gold = ( ------- X 100 ) % = 75%

24

6

Percentage of gold in 6 carat gold = ( ------- X 100 ) % =  25 %

24

12

Percentage of gold in 12 carat gold = ( ------- X 100 ) % =  50 %

24

Let x gm of 18 carat gold and y gm of 16 carat gold be mixed

Then,  x + y = 160 ………………………. (i)

And,  75% of x + 25 % of y =  50% of 160

75 x         25 y          50

=> -------- + -------- = -------- X 160

100          100          100

=>   75 x  +  25 y  =  50 X 160

=>    3 x +  y = 320 …………..……….(ii)

Now, we will subtract (i) from (ii), and we get –

3x + y = 320

x + y = 160

-----------------

2x = 160

=>       x =  80

Now we will substitute x = 80 in (i), and we get –

x + y = 160

=>    80 + y = 160

=>        y =  80

Hence 80 gm of 18-carat gold should be mixed with 80 gm of 6-carat gold to obtain 120 gm of 12-carat gold.   (Ans.)

Example.2) A chemist has one solution containing 75% syrup and a second one containing 50% syrup. How much of each should be used to make 25 liters of a 60% syrup solution?

Ans.)  Let x liters of 75% solution be mixed with y liters of 50% syrup

So, as per the given condition –

x + y =  25  ………………………..(i)

and,  75% of x + 50% of y = 40% of 15

75 x         50 y           60

=> -------- + --------- = -------- X  25

100          100           100

=>     75 x + 50 y = 60 X 25

=>      3 x + 2 y =  60  ……………………………(ii)

Now, we will multiply (i) by 3, and we will get –

3 x + 3 y = 75 ……..……………(iii)

Now, we will substitute (ii) from (iii), and we will get –

3 x + 3 y = 75

3 x + 2 y = 60

------------------

y = 15

now we will substitute y = 15 in (i), and we will get –

x + y  =  25

=>    x + 15 = 25

=>    x  =  10

Hence, 10 liters of 75% solution is to be mixed with 15 liters of 50% solution to make 25 liters of 60% solution.   (Ans.)