-
In a mixture of three varieties of tea, the ratio of their weights is 4 : 5 : 8. If 5 kg tea of the first variety, 10 kg tea of the second variety and some quantity of tea of the third variety are added to the mixture, the ratio of the weights of three varieties of tea becomes as 5 : 7 : 9. In the final mixture, the quantity (in kg) of the third variety of tea was
-
- 42
- 45
- 48
- 40
Correct Option: B
Let quantity of first variety of tea = 4x kg.
Quantity of second variety of tea = 5x kg.
Quantity of third variety of tea = 8x kg.
Let y kg of third variety of tea be mixed.
∴ Resultant ratio = (4x + 5) : (5x + 10) : (8x + y)
| ∴ | = | ||
| 5x + 10 | 7 |
⇒ 28x + 35 = 25 x + 50
⇒ 28x – 25x = 50 – 35
| ⇒ 3x = 15 ⇒ x = | = 5 | |
| 3 |
| ∴ | = | ||
| 8x + y | 9 |
| ⇒ | = | ||
| 8 × 5 + y | 9 |
| ⇒ | = | ||
| 40 + y | 9 |
⇒ 40 + y = 9 × 5
⇒ y = 45 – 40 = 5 kg.
∴ Required quantity of third variety of tea
= 8x + y = 8 × 5 + 5 = 45 kg.
