# In a mixture of petrol and kerosene, petrol is only 99 litres. ## (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%.

Thank You