Govt. Exams
Entrance Exams
Let A, B, C complete work in a, b, c days respectively. 1/a + 1/b = 1/12, 1/b + 1/c = 1/15, 1/a + 1/c = 1/20. Adding all three: 2(1/a + 1/b + 1/c) = 1/12 + 1/15 + 1/20 = 12/60 = 1/5. So 1/a + 1/b + 1/c = 1/10. Therefore, 1/a = 1/10 - 1/15 = 1/30. A completes work in 30 days.
After 20% discount = 1000 × 0.80 = ₹800. After 10% discount = 800 × 0.90 = ₹720
Total distance = 5×3 + 4×2 = 15 + 8 = 23 km. Total time = 5 hours. Avg speed = 23/5 = 4.6 km/h
Amount = 8000 × (1.12)² = 8000 × 1.2544 = ₹10,035.20 (closest is B at ₹10,127.20 - recheck: 8000 × 1.12 × 1.12 = 10,035.20)
Total distance = 200 + 100 = 300 m. Speed = 54 km/h = 15 m/s. Time = 300/15 = 20 seconds
New income = Original × 1.25. 62,500 = Original × 1.25. Original = 62,500/1.25 = ₹50,000
Monthly savings = 50000 × (1-0.60) = ₹20,000. Annual = 20,000 × 12 = ₹240,000
When multiple workers complete a task at different rates, their combined work rate equals the sum of individual rates. The combined rate is found by adding the reciprocals of individual completion times.
Step 1: Find individual work rates
Work rate is the fraction of work completed per day. If A completes work in 8 days, B in 12 days, and C in 16 days:
\[
\text{Rate of A} = \frac{1}{8} \text{ per day}, \quad \text{Rate of B} = \frac{1}{12} \text{ per day}, \quad \text{Rate of C} = \frac{1}{16} \text{ per day}
\]
Step 2: Find combined work rate
When working together, rates add:
\[
\text{Combined rate} = \frac{1}{8} + \frac{1}{12} + \frac{1}{16}
\]
Step 3: Find common denominator and add
The LCM of 8, 12, and 16 is 48:
\[
\frac{1}{8} + \frac{1}{12} + \frac{1}{16} = \frac{6}{48} + \frac{4}{48} + \frac{3}{48} = \frac{13}{48} \text{ per day}
\]
Step 4: Calculate time to complete work
If combined rate is \(\frac{13}{48}\) per day, then time to complete 1 full work is:
\[
\text{Time} = \frac{1 \text{ work}}{\frac{13}{48} \text{ per day}} = \frac{48}{13} \text{ days} \approx 3.69 \text{ days}
\]
Answer: They can complete the work together in \(\frac{48}{13}\) days or approximately 3.69 days (Option D)
Amount = 10000(1.10)² = 10000 × 1.21 = ₹12100. CI = 12100 - 10000 = ₹2100
Relative speed = 40 + 50 = 90 km/h. Distance = 90 × 2 = 180 km
