Question:
Solve the problem based on the given figure.
दिए गए चित्र के आधार पर समस्या को हल करें।
Options:
- a) 2 1/4
- b) 1 3/4
- c) 3 1/2
- d) 2 1/2
- a) 2 1/4
- b) 1 3/4
- c) 3 1/2
- d) 2 1/2
correct answer : d)
Explanation:
Convert the mixed fractions to improper fractions:
\(3\frac{2}{3} = \frac{11}{3}\)
\(2\frac{1}{5} = \frac{11}{5}\)
\(1 – \frac{2}{5} = \frac{3}{5}\)
Now evaluate the bracket:
\(1 + \frac{3}{1 – \frac{2}{5}} = 1 + \frac{3}{\frac{3}{5}} = 1 + 5 = 6\)
Substitute back into the expression:
\(\frac{11}{3} \div \frac{11}{5} \times \frac{1}{4} \times 6\)
\(= \frac{11}{3} \times \frac{5}{11} \times \frac{1}{4} \times 6\)
\(= \frac{5}{3} \times \frac{6}{4} = \frac{30}{12} = \frac{5}{2} = 2\frac{1}{2}\).
मिश्रित भिन्नों को अनुचित भिन्नों में बदलें:
\(3\frac{2}{3} = \frac{11}{3}\)
\(2\frac{1}{5} = \frac{11}{5}\)
\(1 – \frac{2}{5} = \frac{3}{5}\)
अब कोष्ठक (bracket) को हल करें:
\(1 + \frac{3}{1 – \frac{2}{5}} = 1 + \frac{3}{\frac{3}{5}} = 1 + 5 = 6\)
व्यंजक में मान प्रतिस्थापित करें:
\(\frac{11}{3} \div \frac{11}{5} \times \frac{1}{4} \times 6\)
\(= \frac{11}{3} \times \frac{5}{11} \times \frac{1}{4} \times 6\)
\(= \frac{5}{3} \times \frac{6}{4} = \frac{30}{12} = \frac{5}{2} = 2\frac{1}{2}\).