Question

. A container is full of spirit. 40 litres of spirit
is taken out and the container is filled with
water. This process is repeated twice
further. Now, the ratio of spirit to water in
the container is 27:98. Find the capacity of
the container.
1) 95 litres 2) 100 litres 3) 90 litres
4) 105 litres 5) 110 litres​

Answer 1

Given :- A container is full of spirit. 40 litres of spirit is taken out and the container is filled with water. This process is repeated twice further. Now, the ratio of spirit to water in the container is 27:98. Find the capacity of the container.

1) 95 litres

2) 100 litres

3) 90 litres

4) 105 litres

5) 110 litres .

Solution :-

we know that,

• Final concentration (FC) = initial concentration (IC) * (1 - x / V)^n .
• x = Quantity removed .
• V = Total volume..
• n = Number of Process.

given that,

• Final concentration of spirit = 27 /(27 + 98) = (27/125)
• initial concentration of spirit = 1 (Full.)
• x = 40 litres.
• n = 1 + 2 = 3 times.
• V = Let total capacity of container.

Putting all values we get :-

→ (27/125) = 1 * (1 - 40/V)³

→ (3/5)³ = (1 - 40/V)³

cube root both sides,

→ (3/5) = 1 - (40/V)

→ (40/V) = 1 - (3/5)

→ (40/V) = (2/5)

→ 2V = 40 * 5

dividing both sides by 2,

→ V = 20 * 5

→ V = 100 litres. (Option 2) (Ans.)

Hence, the capacity of the container is 100 litres.

Answer 2

Given :- A container is full of spirit. 40 litres of spirit is taken out and the container is filled with water. This process is repeated twice further. Now, the ratio of spirit to water in the container is 27:98. Find the capacity of the container.

1) 95 litres

2) 100 litres

3) 90 litres

4) 105 litres

5) 110 litres .

Solution :-

we know that,

Final concentration (FC) = initial concentration (IC) * (1 - x / V)^n .

x = Quantity removed .

V = Total volume..

n = Number of Process.

given that,

Final concentration of spirit = 27 /(27 + 98) = (27/125)

initial concentration of spirit = 1 (Full.)

x = 40 litres.

n = 1 + 2 = 3 times.

V = Let total capacity of container.

Putting all values we get :-

→ (27/125) = 1 * (1 - 40/V)³

→ (3/5)³ = (1 - 40/V)³

cube root both sides,

→ (3/5) = 1 - (40/V)

→ (40/V) = 1 - (3/5)

→ (40/V) = (2/5)

→ 2V = 40 * 5

dividing both sides by 2,

→ V = 20 * 5

→ V = 100 litres. (Option 2) (Ans.)

Hence, the capacity of the container is 100 litres.