13. Five mark exercise problem - IV

1. If \(A\) \(=\) \(\frac{x}{x + 1}\) and \(B\) \(=\) \(\frac{1}{x + 1}\), then prove that \(\frac{(A + B)^2 + (A - B)^2}{A \div B}\) \(=\) \(\frac{2(x^2 + 1)}{x (x + 1)^2}\).

 

Answer:

 

\((A + B)^2\) \(=\)

 

\((A - B)^2\) \(=\)

 

\(A \div B\) \(=\)

 

\(\frac{(A + B)^2 + (A - B)^2}{A \div B}\)  \(\frac{2(x^2 + 1)}{x (x + 1)^2}\)

 

2. Pari needs \(4\) hours to complete a work. His friend Yuvan needs \(6\) hours to complete the same work. How long will it take to complete if they work together?

 

Answer:

 

Pari and Yuvan will take  hours and  minutes to complete the work.

 

3. Iniya bought \(50 \ kg\) of fruits consisting of apples and bananas. She paid twice as much per \(kg\) for the apple as she did for the banana. If Iniya bought \(₹1800\) worth of apples and \(₹600\) worth of bananas, then how many \(kgs\) of each fruit did she buy?

 

Answer:

 

Quantity of apples bought \(=\)  \(kg\)

 

Quantity of bananas bought \(=\)  \(kg\)