In the fruit market adjacent to IIM lucknow a fruit vendor has total 20 kg of fruits containing only mangoes and apples The vendor told to Ritika an 11M student that one kg apple contains only 7 apples while 1 kg of mangoes contains 10 mangoes and it is known that all the mangoes and apples are uniform in size individually The vendor has initially 176 pieces of apples and mangoes in all Ritika purchases 55 fruits to distribute equally among the group of 11 students irrespective of the kind of fruit i.e.mango or apple and then the vendor is left with only 13 kg of fruits.If the selling price of mangoes and apples be ₹35 per kg and ₹40per kg respectively then how many rupees Ritika has spent for the 7 kg of fruits?

Options

A. 262.5
B. 225
C. 270
D. 155

Answer

To solve the problem step by step, we will follow the information provided in the question and the video transcript.

### Step 1: Understand the total weight of fruits
The vendor has a total of 20 kg of fruits, which consists of mangoes and apples.

### Step 2: Understand the fruit counts
- 1 kg of apples contains 7 apples.
- 1 kg of mangoes contains 10 mangoes.
- Initially, there are 176 pieces of apples and mangoes combined.

### Step 3: Define variables
Let:
- \( x \) = kg of apples
- \( y \) = kg of mangoes

From the problem, we know:
1. \( x + y = 7 \) (since Ritika bought 7 kg of fruits)
2. The total number of fruits can be expressed as \( 7x + 10y = 55 \) (since Ritika bought 55 fruits).

### Step 4: Set up the equations
From the above, we can set up the equations:
1. \( x + y = 7 \)
2. \( 7x + 10y = 55 \)

### Step 5: Solve the equations
From equation (1), we can express \( y \) in terms of \( x \):
\[ y = 7 - x \]

Now, substitute \( y \) into equation (2):
\[ 7x + 10(7 - x) = 55 \]
\[ 7x + 70 - 10x = 55 \]
\[ -3x + 70 = 55 \]
\[ -3x = 55 - 70 \]
\[ -3x = -15 \]
\[ x = 5 \]

Now substitute \( x \) back into equation (1) to find \( y \):
\[ 5 + y = 7 \]
\[ y = 2 \]

### Step 6: Determine the quantities of fruits
- Ritika bought 5 kg of apples and 2 kg of mangoes.

### Step 7: Calculate the cost of the fruits
- The cost of apples is ₹40 per kg.
- The cost of mangoes is ₹35 per kg.

Calculating the total cost:
- Cost of apples: \( 5 \text{ kg} \times 40 \text{ ₹/kg} = 200 \text{ ₹} \)
- Cost of mangoes: \( 2 \text{ kg} \times 35 \text{ ₹/kg} = 70 \text{ ₹} \)

### Step 8: Total cost
Total cost = Cost of apples + Cost of mangoes
\[ = 200 \text{ ₹} + 70 \text{ ₹} = 270 \text{ ₹} \]

### Final Answer
Ritika spent a total of **₹270** for the 7 kg of fruits.

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