A is able to complete a task in 15 days, while B takes 20 days to finish the same task. If they collaborate and work together for 4 days, what fraction of the work will still remain?

A is able to complete a task in 15 days, while B takes 20 days to finish the same task. If they collaborate and work together for 4 days, what fraction of the work will still remain?

A किसी कार्य को 15 दिनों में पूरा कर सकता है, जबकि B उसी कार्य को 20 दिनों में पूरा करता है। यदि दोनों मिलकर 4 दिन कार्य करें, तो कार्य का कितना भाग शेष रहेगा?

Options / विकल्प

A. $\frac{1}{4}$

B. $\frac{7}{15}$

C. $\frac{8}{15}$ ✅

D. $\frac{11}{15}$

Answer / उत्तर

✅ $\frac{8}{15}$

Solution / समाधान

Method 1: Using Work Rates

विधि 1: कार्य-दर का उपयोग

A's one-day work:

\frac{1}{15}

B's one-day work:

\frac{1}{20}

Together, one-day work:

\frac{1}{15}+\frac{1}{20} = \frac{4+3}{60} = \frac{7}{60}

Work done in 4 days:

4\times\frac{7}{60} = \frac{28}{60} = \frac{7}{15}

Remaining work:

1-\frac{7}{15} = \frac{8}{15}

Shortcut Trick / शॉर्टकट ट्रिक

Take total work as:

LCM (15, 20) = 60 units

A's efficiency:

60 \div 15 = 4 \text{ units/day}

B's efficiency:

60 \div 20 = 3 \text{ units/day}

Combined efficiency:

4+3=7 \text{ units/day}

Work done in 4 days:

7\times4=28 \text{ units}

Remaining work:

60-28=32 \text{ units}

Fraction remaining:

\frac{32}{60} = \frac{8}{15}

Final Answer / अंतिम उत्तर

\boxed{\frac{8}{15}}

✅ Correct Answer / सही उत्तर: $\frac{8}{15}$

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