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In what ratio, water must be added to dilute honey costing ₹ 320 per liter so that the resulted syrup would be worth ₹ 280 per liter?

Solution

✅ Correct Option: 3

We have honey at ₹320/liter and water at ₹0/liter. After mixing, the mixture should cost ₹280/liter.

Let water =x= x liters and honey =y= y liters.


When mixed:

Total volume =x+y= x + y liters

Total cost =(x×0)+(y×320)= (x \times 0) + (y \times 320)

Total cost =320y= 320y rupees

Cost per liter of mixture =320yx+y= \frac{320y}{x + y}


The cost per liter must equal ₹280:

320yx+y=280\frac{320y}{x + y} = 280

320y=280(x+y)320y = 280(x + y)

320y=280x+280y320y = 280x + 280y

320y−280y=280x320y - 280y = 280x

40y=280x40y = 280x


Finding the ratio:

40y40y=280x40y\frac{40y}{40y} = \frac{280x}{40y}

1=7xy1 = \frac{7x}{y}

xy=17\frac{x}{y} = \frac{1}{7}

Therefore, water : honey =1:7= 1 : 7

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