Question

8. My mother has prepared two types of sharbat. There is 5 kg sugar in 100 litre sharbat of
the first type and 8 kg sugar in 100 litre sharbat of the second type. By mixing, these two
types. I will prepare 150 litre sharbat which contains 9 5kg sugar. Forming Simultaneous
equation let us calculate how much quantity of two types of sharbat will be mixed to prepare
150 litre sharbat.​

Answer 1

Answer:

The amount of each type of sharbat is given by:

66 $\frac{2}{3}$ kilograms and 83 $\frac{1}{3}$ kilograms

Step-by-step explanation:

Let's calculate the amount of sugar per liter for each of the quantities.

We have:

Type 1:

5/100 = 0.05 kg of sugar per liter

Type 2:

8/100 = 0.08 kg sugar per liter.

Let x be the amount of type 1 and y type 2 mixed to prepare the 150 liter Sharbat.

The amount of sugar in each type is given by:

Type 1 = 0.05x

type 2 = 0.08y

From the information above we form two simulatneous equations as follows:

x + y = 150.....................i

0.05x + 0.08y = 9.5................ii

Multiply ii through by 100 to eliminate the decimals.

x + y = 150......................iii

5x + 8y = 950..................iv

Multiply iii by 5 to get:

5x + 5y = 750

5x + 8y = 950

3y = 200

y = 200/3 = 66 $\frac{2}{3}$ kgs

Substituting in i to get x

x + 200/3 = 150

x = 150 - 200/3 = 83 $\frac{1}{3}$ kgs

Answer 2

The quantity of two types of sharbat will be mixed is 50/3 litre and 400/3 litre.

Solution:

Sharbat of  first type:

$\Rightarrow \frac{5}{100}=\frac{1}{20} \ \mathrm{Kg} / \mathrm{L}$

Sharbat of  second type:

$\Rightarrow \frac{8}{100}=\frac{2}{25} \ \mathrm{Kg} / \mathrm{L}$

We need to find quantity of Sharbat to prepare  150 litre:

Sharbat of  first type = x L

Sharbat of  second type = (150 - x) L

Sugar amount:

$x \frac{1}{20}+\frac{2}{25} x(150-x)=9$

$\frac{x}{20}+12-\frac{2}{25} x= 9$

$x\left(\frac{2}{25} - \frac{1}{20}\right) = 4$

$(\frac{8-5}{100}) x =4$

$(\frac{3}{100}) x = 4$

$x=\frac{400}{3}$

The above is quantity of sharbat.

The quantity of sharbat of  first type:

$150 - \frac{400}{3} =\frac{450-400}{3} = \frac{50}{3} \ L$

The quantity of sharbat of  second type:

$150 - \frac{50}{3} = \frac{450-50}{3} = \frac{400}{3}\ L$