Priya's Fruit Purchase Summary

This problem requires us to calculate the specific amount Priya spent on mangoes. We are given the total weight of fruits (apples and mangoes), the total money spent, and the price per kilogram for each type of fruit. Our task is to isolate the cost related only to the mangoes.

Apples and Mangoes Cost Setup

To tackle this problem systematically, we begin by defining variables for the quantities involved:

• Let $a$ represent the weight of apples purchased, measured in kilograms (kg).
• Let $m$ represent the weight of mangoes purchased, measured in kilograms (kg).

Using the information provided in the question, we can establish two key algebraic equations:

1. Total Weight Equation: The sum of the weights of apples and mangoes is 45 kg. $$a + m = 45$$
2. Total Cost Equation: The total amount spent is ₹1,240. This total cost is the sum of the cost of apples ($25 \times a$) and the cost of mangoes ($30 \times m$). $$25a + 30m = 1240$$

Mango Weight Calculation

The primary objective is to find the cost of mangoes, which is calculated as $30 \times m$. To achieve this, we first need to determine the value of $m$, the weight of mangoes.

We can use the substitution method. Rearranging the Total Weight Equation ($a + m = 45$), we get an expression for the weight of apples ($a$):

$$a = 45 - m$$

Now, we substitute this expression for $a$ into the Total Cost Equation:

$$25(45 - m) + 30m = 1240$$

Distributing the 25 gives:

$$1125 - 25m + 30m = 1240$$

Combine the like terms (the terms with $m$):

$$1125 + 5m = 1240$$

To isolate the term containing $m$, subtract 1125 from both sides:

$$5m = 1240 - 1125$$

$$5m = 115$$

Finally, solve for $m$ by dividing both sides by 5:

$$m = \frac{115}{5}$$

$$m = 23$$

This calculation shows that Priya purchased 23 kg of mangoes.

Mango Expenditure Calculation

With the quantity of mangoes determined, we can now calculate the specific amount of money Priya spent on them. The price of mangoes is ₹30 per kg.

Amount spent on mangoes = Price per kg of mangoes $\times$ Weight of mangoes

Amount spent on mangoes = $30 \times m$

Substituting the value $m = 23$ kg:

Amount spent on mangoes = $30 \times 23$

Amount spent on mangoes = $690$

Therefore, Priya spent ₹690 on mangoes.

Total Cost Verification

To confirm the accuracy of our calculations, let's perform a verification step by checking the total cost.

First, calculate the weight of apples Priya bought:

Weight of apples ($a$) = Total weight - Weight of mangoes ($m$)

$$a = 45 - 23 = 22 \text{ kg}$$

Next, calculate the cost incurred for the apples:

Cost of apples = Price per kg of apples $\times$ Weight of apples

Cost of apples = $25 \times 22$

Cost of apples = $550$

Finally, sum the cost of apples and the cost of mangoes to verify the total expenditure:

Total Expenditure = Cost of apples + Cost of mangoes

Total Expenditure = $550 + 690$

Total Expenditure = $1240$

This calculated total expenditure matches the given total amount of ₹1,240, validating our result for the amount spent on mangoes.