Raj prepares a 60 gm mixture by combining two ingredients X and Y. The cost of ingredient X is ₹80 per 5 gm, and the cost of ingredient Y is ₹80 per 10 gm. Ingredients X and Y are mixed in a manner that the cost of the resulting mixture is ₹14 per gm. What is the quantity of ingredient X (in gm) in the mixture?
Show answer & explanation
Correct answer: A
Explanation
The correct answer is option 1 i.e 45.
Let the quantity of ingredient X = x gm,
Then ingredient Y = (60 − x) gm
Now, total cost of the mixture = 60 gm × ₹14 = ₹840
Now compute cost based on X and Y:
Cost of X = x × 16
Cost of Y = (60 − x) × 8
Total cost = x × 16 + (60 − x) × 8 = ₹840
⇒ 16x + 8(60 − x) = 840 ⇒ 16x + 480 − 8x = 840 ⇒ 8x = 840 − 480 ⇒ 8x = 360
⇒ x = 45