Question

Mixture A and B contain petrol and kerosene in the ratio of 5:4 and 2:1 respectively. 20% Mixture A and 50% mixture of B is mixed form another mixture C. If quantity of petrol in mixture C is 90 litre and ratio of petrol to kerosene in mixture C is 30:19, then find Initial quality of mixture A

Answer 1

Answer:

According to the ratio quantity of A & B must be multiple of 9 & 3 respectively.

Then let's assume A =36ltr & B=15 ltrs.

Quantity of petrol in C = 36*(5/9)*(1/5) + 15*(2/3)*(1/2)=9

9--90 then 36--360

Then initial quantity of A is 360ltrs

Step-by-step explanation:

Answer 2

The initial quantity of mixture A is 360 litres

Step-by-step explanation:

Let the volume of mixture A is $V_A$ and volume of mixture B is $V_B$

Since petrol and kerosene are in ratio 5 : 4 in mixture A

Therefore,

Volume of petrol in mixture A $=\frac{5V_A}{9}$

Volume of kerosene in mixture A $=\frac{4V_A}{9}$

Similarly,

Volume of petrol in mixture B $=\frac{2V_B}{3}$

Volume of kerosene in mixture B $=\frac{V_B}{3}$

if 20% of mixture A and 50% of mixture B is mixed to form mixture C

Then,

Volume of petrol in mixture C = 90 litres

$\implies 90=0.2\times\frac{5V_A}{9}+0.5\times\frac{2V_B}{3}$

$\implies 2\times\frac{5V_A}{9}+5\times\frac{6V_B}{9}=900$

$\implies 10V_A+30V_B=8100$

$\implies V_A+3V_B=810$     ............. (1)

Ratio of petrol and kerosene in the mixture = 30:19

$\implies (0.2\times\frac{5V_A}{9}+0.5\times\frac{2V_B}{3}):(0.2\times\frac{4V_A}{9}+0.5\times\frac{V_B}{3})=30:19$

$\implies (\frac{V_A}{9}+\frac{3V_B}{9}):(\frac{0.8V_A}{9}+\frac{1.5V_B}{9})=30:19$

$\implies \frac{V_A+3V_B}{0.8V_A+1.5V_B}=\frac{30}{19}$

$\implies \frac{V_A+3V_B}{8V_A+15V_B}=\frac{3}{19}$

$\implies 19V_A+57V_B=24V_A+45V_B$

$\implies 5V_A=12V_B$

$\implies V_B=\frac{5V_A}{12}$

Putting the value of $V_B$ in eq (1)

$V_A+3\times\frac{5V_A}{12}=810$

$\implies \frac{V_A(4+5)}{4}=810$

$\implies 9V_A=4\times 810$

$\implies V_A=\frac{4\times 810}{9}$

$\implies V_A=360$ litres

Therefore, the initial quantity of mixture A is 360 litres

Hope this answer is helpful.

Know More:

Q: The concentration of petrol in three different mixtures (petrol and kerosene) is 1/2 , 3/5 and 4/5 respectively. If 2 litres, 3 litres and 1 litre are taken from these three different vessels and mixed. what is the ratio of petrol and kerosene in the new mixture?

Click Here: https://brainly.in/question/5870402