Question

Two vessels X and Y of capacities one and two litres respectively are completely filled with mixtures of 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 to B equal to 1:1?

options are -
1) 1/68 2)1/67 3)1/270 4)1/135​

Answer 1

Answer:

answer would be 1/135

Step-by-step explanation:

in vessel x:

chem A=3/5

chem B=2/5

in vessel B:

chem A=8/9

chem B=10/9

Now In vessel C chem A:chem B=(3/5+8/9):(2/5+10/9) =67:68

we have to add chem A=(68)/(67+68)  -(67)/(67+68)=1/135

Answer 2

Given :-

• Capacities of X : Y = 1 : 2 .
• Ratio of A and B in X = 3 : 2.
• Ratio of A and 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 B in 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,

→ In C , 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.)

Learn more :-

If (x+10)% of 240 is 60% more than x% of 180. then 15% of (x+20) is what percent less than 25% of x?

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