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In the following question, two statements are numbered as I and II. On solving these statements, we get quantities I and II respectively. Solve both quantities and choose the correct option.Statement I . The price of sugar gets increased by 40% and as a result Ram gets 10 kg less sugar. What was the previous consumption?Statement II. The price of rice increased by 50% and thereby 20% increase in the Ram’s expenditure by consuming 12 kg less rice than previous consumption. What was the previous consumption?1.Quantity I ≥ Quantity II2.Quantity I ≤ Quantity II3.Quantity I < Quantity II4.Quantity I > Quantity II5.Quantity I = Quantity II or No relation |
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Answer» Correct Answer - Option 3 : Quantity I < Quantity II Quantity I. Let the price of sugar be Rs. 100 per Kg Let the amount of sugar consumed previously be x kg Total expenditure on sugar previously = 100 × x = Rs. 100x Price increases by 40% New price = Rs 140% of 100 = Rs 140 Consumption of sugar decreases by 10 Kg New consumption = (x – 10) Kg Total expenditure = 140 × (x – 10) = Rs. (140x – 1400) Expenditure remains same ⇒ 140x – 1400 = 100x ⇒ 140x – 100x = 1400 ⇒ 40x = 1400 ⇒ x = 35 Previous consumption = 35 Kg Quantity II. Let the price of sugar be Rs 100 per Kg Let the amount of sugar consumed previously be x Kg Total expenditure = 100 × x = Rs. 100x kg Price increases by 50% New price = 150% of 100 = Rs. 150 Consumption decreases by 12 Kg New consumption = (x – 12) Kg Total expenditure on sugar = 150 × (x – 12) = Rs. (150x – 1800) Expenditure increases by 20% New expenditure on sugar = 120% of 100x = Rs. 120x 120x = 150x – 1800 ⇒ 150x – 120x = 1800 ⇒ 30x = 1800 ⇒ x = 60 Previous consumption = 60 Kg ∴ Quantity II > Quantity I |
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