48 litre of Glycerin is mixed with 144 litre Rose water. D litre of total mixture is taken out and 32 litre Glycerin and 48 litre Rose water are added in the mixture. The final mixture contains 30% Glycerin, find the quantity of the mixture that is taken out.
Question
48 litre of Glycerin is mixed with 144 litre Rose water. D litre of total mixture is taken out and 32 litre Glycerin and 48 litre Rose water are added in the mixture. The final mixture contains 30% Glycerin, find the quantity of the mixture that is taken out.
Solution
Sure, let's solve this step by step:
Step 1: Calculate the initial quantity of Glycerin and Rose water in the mixture.
- Glycerin = 48 litres
- Rose water = 144 litres
- Total mixture = 48 + 144 = 192 litres
Step 2: Let's assume that 'D' litres of the mixture is taken out. This mixture contains Glycerin and Rose water in the same ratio as the initial mixture. So, the quantity of Glycerin and Rose water in 'D' litres of mixture would be:
- Glycerin in 'D' litres = (48/192)*D = D/4 litres
- Rose water in 'D' litres = (144/192)*D = 3D/4 litres
Step 3: Now, 32 litres of Glycerin and 48 litres of Rose water are added. So, the new quantities of Glycerin and Rose water in the mixture would be:
- Glycerin = 48 - D/4 + 32
- Rose water = 144 - 3D/4 + 48
Step 4: According to the problem, the final mixture contains 30% Glycerin. So, the equation would be:
- (Glycerin/Total mixture) = 30/100
- [(48 - D/4 + 32) / (192 - D + 32 + 48)] = 30/100
Step 5: Solve the above equation to find the value of 'D'. The equation simplifies to:
- 4*(80 - D/4) = 3*(272 - D)
- 320 - D = 816 - 3D
- 2D = 496
- D = 248 litres
So, 248 litres of the mixture was taken out.
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