Saved Bookmarks
| 1. |
A mixture contains 60 litre of milk. x litre of solution is taken out and is replaced by water. This process is repeated two times. If the final quantity of milk is 48.6 litres, then find the value of x.1. 9 litres2. 8 litres3. 7 litres4. 6 litres5. None of these |
|
Answer» Correct Answer - Option 4 : 6 litres Given: Initial concentration = 60 litre Final concentration = 48.6 litre Quantity removed in each cycle = x litre The process is repeated two times means: n = 2 Formula: FC = IC × (1 – Quantity removed in each cycle/total IC)n Here, FC = final concentration IC = Initial concentration n = The process repeated how many times Calculation: We know that – FC = IC × (1 – Quantity removed in each cycle/total IC)n …….(1) Put all the given values in equation (1) then we get 48.6 = 60 × (1 – x/60)2 ⇒ 48.6/60 = (1 – x/60)2 ⇒ (486/600) = (1 – x/60)2 ⇒ (81/100)2 = (1 – x/60)2 ⇒ (9/10)2 = (1 – x/60)2 ⇒ 9/10 = 1 – x/60 ⇒ x/60 = 1 – 9/10 ⇒ x/60 = 1/10 ⇒ 10x = 60 ⇒ x = 60/10 ⇒ x = 6 ∴ The Value of x = 6 litres |
|