Question

in vessel P 150 litre of petrol and in vessel Q 150 litre of kerosene if 30 liter from P is taken and poured into Q and again 30 liter taken from Q and poured into P .this process repeated once again .find ratio of petrol and kerosene in P at the end​

Answer 1

13:5 is the ratio of petrol and kerosene in P.

Step-by-step explanation:

Given,

P = 150 l petrol, Q = 150 l Kerosene

ATQ,

Pouring 30 liters from P to Q,

Now, In Q = 150 liters Kerosene + 30 liter petrol

In P, 150 liters petrol - 30 Liters = 120 liters petrol

∵ Kerosene/Petrol = 150/30 = 5:1

Now Pouring 30l from Q to P,

∵ In that 30 Liters,

Petrol = 1/(5 + 1) * 30 = 5liters

Kerosene = 5/6 * 30 = 25liters

Now, In Q = 125 liters Kerosene + 25liters

In P = 125 liters Petrol, 25 liters Kerosene

∵ K:P = 5:1 & P:K = 5:1

Now again 30 liters from P to Q,

In that 30liters = Petrol = 5/(1 + 5) * 30 = 25liters

Kerosene = 1/(1 + 5) * 30 = 5liters

∵ In Q = 130 liters Kerosene + 50 liters petrol

In P = 100 liters petrol + 20 liters Kerosene

Thus, K:P = 13:5 & P:K = 5:1

Now again, 30 liters from Q to P;

∵ In that 30 liters;

Petrol = 5/(13 + 5) * 30 = 25/3 liters

Kerosene = 13/18 * 30 = 65/3 liters

In P,

Petrol = 100 + 25/3 = 325/3 liters

Kerosene = 20 + 65/3 = 125/3 liters

∵ P:K = 325/3 ÷ 125/3 = 13:5

Thus, the ratio of petrol and kerosene in P at the end​ is 13:5.

Learn more: find the ratio

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