Question

two vessels x and y of capacities one and two litres respectively and completely filled with mixtureof two chemicals a and b the ratio by volume of the chemicals a and b in x and y are 3:2 and 4:5 respectively the contents of a and b are mixed and the combination is kept in a vessel c of capacity of four litres how many litres of chemical a should be added to the combination so as to make the ratio of a and b equal to 1:1

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Answer 1

Answer:

Step-by-step explanation:

1/68

Answer 2

Given :

• Capacities of X:Y = 1:2.
• Ratio of Aand B in X = 3: 2.
• Ratio of Aand B in Y = 4:5.
• Capacity of C = 4 litre.
• Ratio of A and B in C = 1:1.

Solution :

As given that, capacity of X is 1 litre and Ratio of A and B in X is 3: 2.

So,

→ chemical A quantity in 1 litre of X =1* (3 out of 5) = (3/5) litre.

Similarly,

→chemical B quantity in 1 litre of X =1* (2 out of 5) = (2/5) litre.

Now, we have given that, capacity of Y is 2 litre and Ratio of A and Bin Y is 4: 5.

So,

→ chemical A quantity in 2 litre of Y = 2 * (4 out of 9) = (8/9) litre.

Similarly,

→ chemical B quantity in 2 litre of Y = 2 * (5 out of 9) = (10/9) litre.

Now, we have given that, The contents of A and B are mixed and the combination is kept in a vessel C of capacity of 4 litres.

Therefore,

→ In vessel C out of 4 litre , total quantity of A= (quantity of A in X + quantity of A in Y) = (3/5 + 8/9) = (27 + 40)/45 = (67/45) Litres.

Similarly,

→ In vessel C out of 4 litre , total quantity of B= (quantity of B in X + quantity of B in Y) = (2/5 + 10/9) = (18 + 50)/45 = (68/45) Litres.

Hence, In vessel C , A: B = (67/45) : (68/45) = 67: 68.

But now, we have to add some more chemical A so that, ratio of A and B becomes equal. {1:1}.

So,

→ InC, Capacity of B = 68/(67+68) = (68/135) litres.

→ In C, capacity of A = 67/(67 + 68) = (67/135) litres.

Thus,

→ Chemical A must be added to make Equal to B = (68/135) - (67/135) = (1/135) Litres. (Ans.)

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