Directions () : Study the following information carefully and answer the given questions
. Aman prints visiting cards of four standard sizes - `(L xx 2)` sq cm, `(6 xx 3)` sq cm, `(5 xx 5)` sq cm and `(2 xx 2)` sq cm. On Monday he printed cards of two sizes `(L xx 2)` sq cm and `(6 xx 3)` sq cm for a client. The respective ratio between the number of `(L xx 2)` sq cm cards and the number of `(6 xx 3)` sq cm cards printed on Monday was 2:3. The client had to pay a total of rs 1600 for the `(L xx 2)` sq cm card and a total of rs 5400 for `(6 xx 3)` sq cm card, (Both at the rate of 2 rs per sq. cm).
On Friday, Aman printed only `(6 xx 3)` sq cm size cards. The total number of cards printed was 90 more than that printed on Monday at the rate of 5 rs per sq cm. Find the total cost incurred, (in rs)

Options

A. 30600
B. 31600
C. 32500
D. 33600

Answer

To solve the problem step by step, we can follow these calculations:

### Step 1: Understand the sizes and costs of the cards
Aman prints visiting cards of four sizes:
1. \( L \times 2 \) sq cm
2. \( 6 \times 3 \) sq cm
3. \( 5 \times 5 \) sq cm
4. \( 2 \times 2 \) sq cm

The costs are given at the rate of Rs. 2 per sq cm for the cards printed on Monday.

### Step 2: Calculate the area of each card size
- Area of \( L \times 2 \) = \( 2L \) sq cm
- Area of \( 6 \times 3 \) = \( 18 \) sq cm
- Area of \( 5 \times 5 \) = \( 25 \) sq cm
- Area of \( 2 \times 2 \) = \( 4 \) sq cm

### Step 3: Determine the number of cards printed on Monday
Let the number of \( L \times 2 \) cards printed be \( 2x \) and the number of \( 6 \times 3 \) cards printed be \( 3x \) (based on the ratio 2:3).

### Step 4: Calculate the total cost for each card type printed on Monday
- Total cost for \( L \times 2 \) cards:
\[ \text{Cost} = \text{Area} \times \text{Rate} \times \text{Number of cards} = (2L) \times 2 \times (2x) = 8Lx \]

- Total cost for \( 6 \times 3 \) cards:
\[ \text{Cost} = 18 \times 2 \times (3x) = 108x \]

Given that the total cost for \( L \times 2 \) cards is Rs. 1600 and for \( 6 \times 3 \) cards is Rs. 5400, we can set up the equations:
1. \( 8Lx = 1600 \)
2. \( 108x = 5400 \)

### Step 5: Solve for \( x \)
From the second equation:
\[ x = \frac{5400}{108} = 50 \]

### Step 6: Substitute \( x \) back to find \( L \)
From the first equation:
\[ 8L(50) = 1600 \implies 400L = 1600 \implies L = 4 \]

### Step 7: Calculate the total number of cards printed on Monday
Total cards printed on Monday:
\[ 2x + 3x = 5x = 5 \times 50 = 250 \]

### Step 8: Determine the number of cards printed on Friday
On Friday, Aman printed 90 more cards than on Monday:
\[ \text{Total cards on Friday} = 250 + 90 = 340 \]

### Step 9: Calculate the cost of cards printed on Friday
The cards printed on Friday were all \( 6 \times 3 \) cards, with a cost of Rs. 5 per sq cm:
\[ \text{Cost of one } 6 \times 3 \text{ card} = 18 \times 5 = 90 \text{ Rs.} \]

Total cost for 340 cards:
\[ \text{Total Cost} = 340 \times 90 = 30600 \text{ Rs.} \]

### Final Answer
The total cost incurred for the cards printed on Friday is Rs. 30,600.

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