A 20 litre solution contains oil and kerosene in the ratio 3:5. If 4 litres of…
2024
A 20 litre solution contains oil and kerosene in the ratio 3:5. If 4 litres of mixture is replaced with 4 litres of kerosene, what will be the ratio of oil and kerosene?
- A.
3/7
- B.
2/7
- C.
1/2
- D.
1/3
Show answer & explanation
Correct answer: A
Concept: When a fixed volume is removed from a mixture, every component in it is removed in the same proportion in which it is present in the mixture — only a substance that is explicitly added afterward changes independently of that ratio.
In the 20 litre mixture, oil : kerosene = 3 : 5, so oil = (3/8) × 20 = 7.5 litres and kerosene = (5/8) × 20 = 12.5 litres.
When 4 litres of this mixture is removed, it is removed in the same 3 : 5 ratio: oil removed = (3/8) × 4 = 1.5 litres and kerosene removed = (5/8) × 4 = 2.5 litres.
Remaining oil = 7.5 − 1.5 = 6 litres. Remaining kerosene = 12.5 − 2.5 = 10 litres.
The 4 litres removed is replaced with 4 litres of kerosene, so the final kerosene quantity = 10 + 4 = 14 litres; oil stays at 6 litres.
Final ratio of oil to kerosene = 6 : 14 = 3 : 7.
Cross-check: the total volume after the operation is 6 + 14 = 20 litres, matching the original 20 litre solution (4 litres were removed and 4 litres added back), confirming the working is consistent.