In what ratio water must be added to dilute honey costing Rs.240 per litre so that resulting syrup would be Rs.180 per litre
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → \(1:3\)
Water costs nothing. Let x litres of water be mixed with y litres of honey. The cost of the mixture is the cost of the honey alone:
\(240y = 180(x + y)\)
\(60y = 180x\)
\( \displaystyle \frac{x}{y} = \frac{60}{180} = \frac{1}{3} \)
So water and honey are mixed in the ratio water : honey = 1 : 3.
By the rule of alligation: water : honey \(= (240 - 180) : (180 - 0) = 60 : 180 = 1 : 3\).
Why the other options are incorrect
Option (2) \(4:3\) — Incorrect. 4 litres of water with 3 litres of honey cost \(\frac{240 \times 3}{7} = 102.86\) per litre, not 180.
Option (3) \(3:1\) — Incorrect. This is the ratio honey : water, the reverse of the ratio asked.
Option (4) \(3:4\) — Incorrect. 3 litres of water with 4 litres of honey cost \(\frac{240 \times 4}{7} = 137.14\) per litre, not 180.