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: Write every quantity in terms of T.
Let the quantity of T sold be $t$. From the given ratios, S $= 2t$, R $= 3t$, and Q $= 4t$.
Since 250 items were sold in total, the quantity of P is \( P = 250 - t - 2t - 3t - 4t = 250 - 10t \).

Step 2: Use the average selling price to form an equation.
Total revenue equals average price times total items, so \( 100P + 50Q + 40R + 60S + 60T = 60 \times 250 = 15000 \).
Substituting the quantities in terms of $t$ gives \( 100(250 - 10t) + 50(4t) + 40(3t) + 60(2t) + 60t = 15000 \).

Step 3: Solve for t, then find P.
Expanding gives \( 25000 - 1000t + 200t + 120t + 120t + 60t = 15000 \), which simplifies to \( 25000 - 500t = 15000 \).
This gives \( t = 20 \), so \( P = 250 - 10(20) = 50 \).

Final Answer:
The quantity of product P sold that day is 50, which matches the given revenue exactly.\[ \boxed{P = 50} \]