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When the price of sugar increased by 28%, a family reduced its consumption per month such that the expenditure on sugar was only 12% more than the earlier one. If the family consumed 18.4 kg of sugar per month earlier, then what is its new consumption of sugar per month?

When the price of sugar increased by 28%, a family reduced its consumption per month such that the expenditure on sugar was only 12% more than the earlier one. If the family consumed 18.4 kg of sugar per month earlier, then what is its new consumption of sugar per month? Correct Answer 16.1 kg

Short trick:

Let consumption of sugar be x kg.

⇒ x = (112/128) × 18.4 = 16.1 kg

Detailed Solution:

Let the price of sugar be 100x.

Price of sugar after increment = 100x × (128/100) = 128x

Price ratio of sugar = 100x : 128x

Consumption is inversely proportional to price.

Consumption ratio of sugar before to after = 128x : 100x

New price of sugar if family wants to increase in expenditure on sugar 12% only

= 100x × (112/100) = 112x

Now price ratio of sugar = 100x : 112x

Now Consumption ratio of sugar before to after = 112x : 100x

⇒ Consumption ratio of sugar before, at 12% increase in price and at 28% increase in price

= 128x : 112x : 100x

⇒ 128x = 18.4 kg

⇒ x = 18.4/128

⇒ 112x = (18.4/128) × 112 = 16.1 kg

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