Discussion
The table lists the unit selling price of five products P, Q, R, S, and T. On a particular day, 250 items were sold with the average selling price of Rs. 60. The following observations were made:
(i) The quantity of S sold was twice that of T.
(ii) The quantity of R sold was thrice that of T.
(iii) The quantity of Q sold was four times that of T.
What is the quantity of product P sold on that day?
| Product | P | Q | R | S | T |
| Unit selling price (Rs.) | 100 | 50 | 40 | 60 | 60 |
Answer: B
The quantity of P sold is 50.
Let \(t\) items of T be sold. Then S, R and Q sold \(2t, 3t, 4t\), and P sold \(p\). Total revenue is \(250 \times 60 = 15000\).
\[ \begin{aligned} p + 10t &= 250 \\ 100p + 50(4t) + 40(3t) + 60(2t) + 60t &= 15000 \\ 100p + 500t &= 15000 \end{aligned} \]
Substituting \(p = 250 - 10t\): \(25000 - 1000t + 500t = 15000\), so \(t = 20\) and \(p = 50\). Check: \(5000 + 4000 + 2400 + 2400 + 1200 = 15000\). The values 40, 60 and 70 do not satisfy both the item count and the revenue.
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