The demand for a good is q = 50 - 2p. At a price of Rs 10, the total expenditure on the good is Rs 300. At which other price is the total expenditure on the good also Rs 300?
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → Rs 15
Expenditure = price × quantity demanded. Set p(50 − 2p) equal to 300 and solve for p.
\( \displaystyle p(50 - 2p) = 300 \)
\( \displaystyle 2p^2 - 50p + 300 = 0 \)
\( \displaystyle p^2 - 25p + 150 = 0 \)
\( \displaystyle (p - 10)(p - 15) = 0 \)
\( \displaystyle p = 10 \text{ or } p = 15 \)
Check: at Rs 15, q = 50 − 30 = 20 and 15 × 20 = 300
The other price is Rs 15.
NCERT (2026-27): “2.6.3 Elasticity and Expenditure The expenditure on a good is equal to the demand for the good times its price. Often it is important to know how the expenditure on a good changes as a result of a price change. The price of a good and the demand for the good are inversely related to each other. Whether the expenditure on the good goes up or down as a result of an increase in its price depends on how responsive the demand for the good is to the price change. …” |