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 the quantities of Q, R, S in terms of T, then use both the total item count (250) and the total revenue (250 x 60) to form two equations in P's quantity and T.

Answer 1

The Correct Option is B

Step 1: Set up variables for each product's quantity.
Let the quantity of T sold be \(t\). From the observations,
Quantity of S \(= 2t\), Quantity of R \(= 3t\), Quantity of Q \(= 4t\).
Let the quantity of P sold be \(p\), which is what we need to find.

Step 2: Write the total-items equation.
The total number of items sold that day is \(250\), so
\[ p + 4t + 3t + 2t + t = 250 \]
\[ p + 10t = 250 \quad \text{...(1)} \]

Step 3: Write the total-revenue equation.
The average selling price was Rs. \(60\) over \(250\) items, so the total revenue that day was
\[ 250 \times 60 = 15000 \]
Revenue is quantity times unit price, added across all five products:
\[ 100p + 50(4t) + 40(3t) + 60(2t) + 60(t) = 15000 \]
\[ 100p + 200t + 120t + 120t + 60t = 15000 \]
\[ 100p + 500t = 15000 \quad \text{...(2)} \]

Step 4: Solve the two equations together.
From equation (1), \(p = 250-10t\). Substitute this into equation (2):
\[ 100(250-10t) + 500t = 15000 \]
\[ 25000 - 1000t + 500t = 15000 \]
\[ 25000 - 500t = 15000 \]
\[ 500t = 10000 \implies t = 20 \]

Step 5: Find \(p\).
\[ p = 250 - 10(20) = 250-200 = 50 \]
So the quantity of product P sold that day is \(50\).

Step 6: Quick check.
With \(t=20\): Q\(=80\), R\(=60\), S\(=40\), T\(=20\), P\(=50\), total \(=50+80+60+40+20=250\), correct. Revenue \(=100(50)+50(80)+40(60)+60(40)+60(20)=5000+4000+2400+2400+1200=15000\), matching Rs. \(60\) average over \(250\) items.

Step 7: Final Answer.
\[ \boxed{p = 50} \]