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 rs1600 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 rs 2 per sq. cm).
How much cards aman print `(6xx3)` sq cm size on monday?

Options

A. 105
B. 120
C. 75
D. 150

Answer

To solve the problem, we need to find out how many `(6 xx 3)` sq cm cards Aman printed on Monday. Let's break down the information step by step.

### Step 1: Understand the sizes and costs
- Aman prints cards of sizes `(L xx 2)` sq cm and `(6 xx 3)` sq cm.
- The cost of printing is Rs 2 per sq cm.

### Step 2: Calculate the area of each card
1. For the `(L xx 2)` sq cm card:
- Area = L * 2 sq cm (we will find L later)
2. For the `(6 xx 3)` sq cm card:
- Area = 6 * 3 = 18 sq cm

### Step 3: Set up the ratio of cards printed
- The ratio of the number of `(L xx 2)` sq cm cards to `(6 xx 3)` sq cm cards is given as 2:3.
- Let the number of `(L xx 2)` sq cm cards be `2x` and the number of `(6 xx 3)` sq cm cards be `3x`.

### Step 4: Calculate the total cost for each card type
1. Total cost for `(L xx 2)` sq cm cards:
- Total cost = Rs 1600
- Cost per card = Area * Rate
- Therefore, for `(L xx 2)` sq cm cards:
\[ \text{Total cost} = (L * 2) * 2x = 1600 \]
Simplifying gives:
\[ 4xL = 1600 \implies xL = 400 \implies L = \frac{400}{x} \]

2. Total cost for `(6 xx 3)` sq cm cards:
- Total cost = Rs 5400
- Therefore, for `(6 xx 3)` sq cm cards:
\[ \text{Total cost} = (18) * (3x) * 2 = 5400 \]
Simplifying gives:
\[ 108x = 5400 \implies x = \frac{5400}{108} = 50 \]

### Step 5: Calculate the number of `(6 xx 3)` sq cm cards printed
- Now that we have `x = 50`, we can find the number of `(6 xx 3)` sq cm cards:
\[ \text{Number of } (6 xx 3) \text{ cards} = 3x = 3 * 50 = 150 \]

### Final Answer
Aman printed **150** cards of size `(6 xx 3)` sq cm on Monday.

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