Initial Stock Composition
Let $T$ represent the total stock (in kg) at the beginning.
Initially, product A constituted 80% of the total stock.
- Initial quantity of Product A: $A_{initial} = 0.80 \times T$
- Initial quantity of Product B: $B_{initial} = (1 - 0.80) \times T = 0.20 \times T$
Stock Changes and Final Ratio
Following the removal of specific quantities:
- Product A removed: 20 kg
- Product B removed: 8 kg
The quantities remaining in the stock are:
- Final quantity of Product A: $A_{final} = (0.80T - 20)$ kg
- Final quantity of Product B: $B_{final} = (0.20T - 8)$ kg
The ratio of the final quantities of Product A to Product B is given as 9 : 2.
We can express this relationship as an equation:
$ \frac{A_{final}}{B_{final}} = \frac{9}{2} $Substituting the expressions for $A_{final}$ and $B_{final}$:
$ \frac{0.80T - 20}{0.20T - 8} = \frac{9}{2} $Solving for the Initial Total Stock
To find $T$, we solve the equation:
Cross-multiply the terms:
$ 2 \times (0.80T - 20) = 9 \times (0.20T - 8) $ $ 1.60T - 40 = 1.80T - 72 $Rearrange the equation to isolate $T$:
$ 72 - 40 = 1.80T - 1.60T $ $ 32 = 0.20T $Calculate the value of $T$:
$ T = \frac{32}{0.20} $ $ T = \frac{320}{2} $ $ T = 160 $The total stock in the beginning was 160 kg.
Similar Questions
- A sample of milk from a vessel contains 4% water. What quantity of pure milk should be added to 8 L of milk in the vessel to reduce the water content to 2%?
- A sample of milk contains 5% of water. What quantity of pure milk should be added to 10 L of milk sample to reduce this to 2%?
- Geeta is decorating the cover of her school magazine. She is allowed to use only three colours from a group of six colours (P, Q, R, S, T and U), based on the following conditions.
I. If P, Q or R is chosen, U cannot be chosen.
II. Either T or U must be chosen.
III. S and Q cannot be chosen together.
If R is chosen, which of the following pairs of colours must also be chosen? - How much of an $80\%$ orange juice drink must be mixed with 36 litres of a $25\%$ orange juice drink to obtain a mixture that has $60\%$ orange juice?
- A mixture contains alcohol and water in the ratio of $5 : 4$. If 9 litres of water is added to the mixture, the ratio of alcohol to water becomes $4 : 5$. Find the quantity of alcohol in the mixture.
- In mixture A, there is 5 L of syrup in 6 L of water. In mixture B, there is 3.5 L of syrup in 5.5 L of water. In which of the two mixtures is the concentration of syrup greater?
- In a mixture of milk and water of 120 litres, the ratio of milk to water is $2:1$. If the ratio of milk to water needs to be $1:2$, then the amount of water that needs to be added to the mixture is:
- A milkman mixes 10% water in pure milk but he is not content with it. So, he again mixes 10% more water in the previous mixture. What is the profit percentage of milk if he sells it at cost price?
- 85L of a mixture contains milk and water in the ratio 27 : 7. How much more water should be added to get a new mixture containing milk and water in the ratio 3 : 1?
- A dairy man purchases at ₹6.40 per litre of milk. He adds water and sells the mixture at ₹8 per litre, thereby making 37.5% profit. The ratio of water to milk received by his customer is:
Important Questions from Mixture and Alligation
My father is presently 25 years older than me. The sum of our ages 5 years ago was 39 years. Find my present age.
Rice worth ₹43/kg and ₹67/kg are mixed with a third variety in the ratio 2 : 1 : 5. If the mixture is worth ₹96/kg, the price (in ₹) of the third variety of rice per kg will be:
42 litres of milk at ₹25 per litre is mixed with 28 litres of milk at ₹40 per litre. Find the average price of the mixture.
15 kg of ₹10 per kg wheat is mixed with 5 kg of another type of wheat to get a mixture costing ₹30 per kg. Find the price (per kg) of the costlier wheat.
If a + b + c = 0, then the value of (a² + b² + 2ab) is equal to:
