In a mixture of petrol and kerosene, petrol is only 99 litres.
Posted on 21-02-2023
Ques - In a mixture of petrol and kerosene, petrol is only 99 litres. If this same quantity of petrol would be presented in another mixture of petrol and Kerosene where total volume would be 198 litres less than the actual mixture then the concentration of petrol in the actual mixture would have been 13.33% point less than that of the new mixture. What is the concentration of petrol in actual mixture ?
(a) 20%
(b) 16.66%
(c) 26.66%
(d) 8.33%
Solution -
In a mixture of petrol and kerosene,
The petrol = 99
Let,
The kerosene = x
Total mixture of petrol and kerosene = 99 + x
In another mixture of petrol and Kerosene,
Where,
Total volume would be 198 litres less than the actual mixture.
The petrol = 99 (same quantity)
The kerosene = x - 198
Total mixture = 99 + x - 198
= x - 99
Then,
The concentration of petrol in the actual mixture would have been 13.33% point less than that of the new mixture.
A/C
[99 / (x - 99) × 100] - [99 / (x + 99) × 100] = 13.33
[9900 / (x - 99)] - [ 9900 / (x + 99)] = 13.33
9900 [1 / (x - 99) - 1 / (x + 99)] = 13.33
9900 [ (x + 99 - x + 99) / (x² - 99²)] = 13.33
[9900 (198)] / (x² - 99²) = 40/3
x² - 99² = 99² × 15
x² - 9801 = 9801 × 15
x² - 9801 = 147015
x² = 147015 + 9801
x² = 156816
x = (156816)½
x = 396
Thus,
The kerosene = 396 litres
Total mixture = 99 + x
= 99 + 396
= 495 litres
Therefore,
The actual concentration of petrol = [99 / (495)] × 100
= 9900 / 495
= 20%
Hence,
The correct answer is option (a) 20%.
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