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Fraction of Work Done / Remaining

Introduction

Time and Work problems में अक्सर यह जानना ज़रूरी होता है कि किसी समय तक काम का कौन-सा fraction पूरा हुआ है या कितना बाकी है। यह pattern तब मदद करता है जब काम आंशिक समय में हो रहा हो या कुछ workers बीच में आते-जाते हों।

यह concept progress tracking, efficiency analysis और mid-way join/leave वाले questions समझने के लिए बहुत उपयोगी है।

Pattern: Fraction of Work Done / Remaining

Pattern

Key idea: Work done = Time taken ÷ Total time.

इसी तरह, Fraction of work remaining = 1 - (Time taken ÷ Total time).

Step-by-Step Example

Question

A कोई काम 15 days में पूरा करता है। 9 days बाद वह काम का कितना fraction पूरा करेगा? और कितना fraction बाकी रहेगा?

Solution

  1. Step 1: दिए गए values पहचानें

    Time taken = 9 days; Total time = 15 days.

  2. Step 2: Fraction of work done निकालें

    Fraction of work done = Time taken ÷ Total time = 9 ÷ 15 = 3/5.

  3. Step 3: Remaining fraction निकालें

    Work remaining = 1 - 3/5 = 2/5.

  4. Final Answer:

    Work done = 3/5; Work remaining = 2/5.

  5. Quick Check:

    पूरी 15 days बाद: 15 ÷ 15 = 1 (complete work) ✅

Quick Variations

1. कुछ दिनों बाद कितना work बचा है, यह निकालना।

2. किसी दिए गए fraction का work पूरा करने में कितना time लगेगा, यह निकालना।

3. Multiple workers के join/leave होने पर combined fraction problems।

4. Pipes & Cistern या efficiency-based mixed work questions में भी यही concept उपयोग होता है।

Trick to Always Use

  • Step 1: Fraction done निकालने के लिए हमेशा time taken ÷ total time का उपयोग करें।
  • Step 2: Remaining fraction पाने के लिए बस 1 में से subtract करें।
  • Step 3: Multiple workers हों तो पहले उनकी combined rate से total time निकालें।

Summary

Summary

Fraction of Work Done / Remaining pattern में:

  • Work done = Time taken ÷ Total time.
  • Work left = 1 - Work done.
  • Progress tracking और partial completion वाले problems में बहुत उपयोगी।

Practice

(1/5)
1. A can complete a work in 12 days. What fraction of the work will be completed in 3 days?
easy
A. 1/3
B. 1/4
C. 1/2
D. 1/6

Solution

  1. Step 1: Identify given values

    Total time = 12 days; time taken = 3 days.

  2. Step 2: Compute fraction of work done

    Fraction of work done = 3 ÷ 12 = 1/4.

  3. Final Answer:

    Work done = 1/4 → Option B.

  4. Quick Check:

    3 × (1/12) = 3/12 = 1/4 ✅
Hint: Divide time taken by total time to get fraction done.
Common Mistakes: Using full-time instead of partial time or failing to simplify the fraction.
2. B can do a job in 10 days. What fraction of the work remains after 6 days of work?
easy
A. 2/5
B. 1/5
C. 3/5
D. 4/5

Solution

  1. Step 1: Identify given values

    Total time = 10 days; time worked = 6 days.

  2. Step 2: Compute work done

    Work done = 6 ÷ 10 = 3/5.

  3. Step 3: Compute remaining work

    Remaining = 1 - 3/5 = 2/5.

  4. Final Answer:

    Work left = 2/5 → Option A.

  5. Quick Check:

    60% done → 40% left = 2/5 ✅
Hint: Remaining work = 1 - (fraction completed).
Common Mistakes: Adding fractions instead of subtracting from 1.
3. A can finish a work in 15 days. What fraction of the work will A complete in 5 days?
easy
A. 1/2
B. 1/4
C. 1/3
D. 2/3

Solution

  1. Step 1: Identify given values

    Total time = 15 days; time taken = 5 days.

  2. Step 2: Compute fraction completed

    Fraction = 5 ÷ 15 = 1/3.

  3. Final Answer:

    Work completed = 1/3 → Option C.

  4. Quick Check:

    5 × (1/15) = 1/3, matches result ✅
Hint: Fraction = time taken ÷ total time.
Common Mistakes: Incorrect simplification of 5/15.
4. A and B together can finish a work in 8 days. They work together for 3 days. What fraction of the work remains?
medium
A. 5/8
B. 3/8
C. 1/2
D. 1/4

Solution

  1. Step 1: Identify time worked

    Total time = 8 days; worked time = 3 days.

  2. Step 2: Compute fraction completed

    Completed = 3 ÷ 8 = 3/8.

  3. Step 3: Compute fraction remaining

    Remaining = 1 - 3/8 = 5/8.

  4. Final Answer:

    Remaining work = 5/8 → Option A.

  5. Quick Check:

    Done 3/8; left 5/8 → total = 1 ✔
Hint: Fraction done = worked_days / total_days.
Common Mistakes: Subtracting wrongly or confusing done vs remaining.
5. A can complete a work in 18 days and B can complete the same work in 12 days. Working together, what fraction of the work will be completed in 6 days?
medium
A. 1/2
B. 3/5
C. 2/3
D. 5/6

Solution

  1. Step 1: Compute individual daily rates

    A's rate = 1/18, B's rate = 1/12.

  2. Step 2: Compute combined daily work

    Combined = 1/18 + 1/12 = (2 + 3)/36 = 5/36.

  3. Step 3: Work done in 6 days

    6 × (5/36) = 30/36 = 5/6.

  4. Final Answer:

    Work completed = 5/6 → Option D.

  5. Quick Check:

    Remaining = 1 - 5/6 = 1/6 ✔
Hint: Add one-day works, then multiply by days worked.
Common Mistakes: Adding days instead of rates.

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