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:

Use the ratio clues to write everyone's quantity in terms of T's quantity, then solve total-quantity and total-revenue equations together.

Answer 1

The Correct Option is B

Step 1: Set up variables using the ratio clues.
Let the quantity of T sold be \(t\).
From clue (i), quantity of S \(= 2t\).
From clue (ii), quantity of R \(= 3t\).
From clue (iii), quantity of Q \(= 4t\).
Let the quantity of P sold be \(p\), the value we need to find.

Step 2: Write the total quantity equation.
The total number of items sold is 250, so
\[ p + 4t + 3t + 2t + t = 250 \]
\[ p + 10t = 250 \]

Step 3: Write the total revenue equation.
Average selling price is Rs. 60 over 250 items, so total revenue \(= 250 \times 60 = 15000\).
Using the unit prices from the table (P=100, Q=50, R=40, S=60, T=60):
\[ 100p + 50(4t) + 40(3t) + 60(2t) + 60(t) = 15000 \]
\[ 100p + 200t + 120t + 120t + 60t = 15000 \]
\[ 100p + 500t = 15000 \]

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

Step 5: Find the quantity of P.
\[ p = 250 - 10t = 250 - 10(20) = 250 - 200 = 50 \]
As a check, quantities are P=50, Q=80, R=60, S=40, T=20, total \(=50+80+60+40+20=250\), matching the given total, and revenue \(=50(100)+80(50)+60(40)+40(60)+20(60) = 5000+4000+2400+2400+1200=15000\), matching Rs. \(60 \times 250\).

Final Answer:
The quantity of product P sold is 50, option (B). \[ \boxed{p = 50} \]