Question

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.

Product	P	Q	R	S	T
Unit selling price (Rs.)	100	50	40	60	60

What is the quantity of product P sold on that day?

• A. 40
• B. 50
• C. 60
• D. 70

Hint:

Write every quantity in terms of T, then use the total revenue equation.

Answer 1

The Correct Option is B

Step 1: Fix the quantities of Q, R, S, T using one unknown.
Take T's quantity as $n$. Then S $= 2n$, R $= 3n$, Q $= 4n$, so these four items total $n + 2n + 3n + 4n = 10n$.
The remaining items are P, so P's quantity is $250 - 10n$.

Step 2: Check revenue against the known average.
The 250 items sold for an average of Rs. 60 each, so the total money collected is $250 \times 60 = 15000$ rupees.
Writing each product's contribution: P gives $100(250 - 10n)$, Q gives $50 \times 4n = 200n$, R gives $40 \times 3n = 120n$, S gives $60 \times 2n = 120n$, T gives $60n$.

Step 3: Add everything and solve.
Adding all contributions: $25000 - 1000n + 200n + 120n + 120n + 60n = 15000$, so $25000 - 500n = 15000$, giving $n = 20$.
So P's quantity is $250 - 200 = 50$, and a quick check confirms the revenue: $50(100)+80(50)+60(40)+40(60)+20(60) = 15000$.

Final Answer:
The quantity of P sold works out to 50 units.\[ \boxed{P = 50} \]