Total Number of Bananas

Video Explanation

Question

Vijay divided his bananas into two lots A and B.

Lot A was sold at the rate of Rs 2 for 3 bananas. Lot B was sold at the rate of Rs 1 per banana. Total collection = Rs 400.

If Lot A had been sold at Rs 1 per banana and Lot B at Rs 4 for 5 bananas, the total collection would have been Rs 460.

Find the total number of bananas.

Solution

Step 1: Let the Variables

Let number of bananas in Lot A = \(x\)

Let number of bananas in Lot B = \(y\)

Step 2: Convert Rates into Per Banana Form

Rs 2 for 3 bananas \[ \text{Rate per banana} = \frac{2}{3} \]

Rs 4 for 5 bananas \[ \text{Rate per banana} = \frac{4}{5} \]

Step 3: Form the Equations

First condition:

\[ \frac{2}{3}x + y = 400 \quad (1) \]

Second condition:

\[ x + \frac{4}{5}y = 460 \quad (2) \]

Step 4: Remove Fractions

Multiply equation (1) by 3:

\[ 2x + 3y = 1200 \quad (3) \]

Multiply equation (2) by 5:

\[ 5x + 4y = 2300 \quad (4) \]

Step 5: Solve by Elimination Method

Multiply equation (3) by 5:

\[ 10x + 15y = 6000 \quad (5) \]

Multiply equation (4) by 2:

\[ 10x + 8y = 4600 \quad (6) \]

Subtract (6) from (5):

\[ (10x + 15y) – (10x + 8y) = 6000 – 4600 \]

\[ 7y = 1400 \]

\[ y = 200 \]

Step 6: Find the Value of x

Substitute \(y = 200\) in equation (3):

\[ 2x + 3(200) = 1200 \]

\[ 2x + 600 = 1200 \]

\[ 2x = 600 \]

\[ x = 300 \]

Conclusion

Bananas in Lot A = 300
Bananas in Lot B = 200

Total bananas:

\[ \boxed{300 + 200 = 500} \]

Final Answer (For Exam)

Total number of bananas = 500