Parimal completes one fourth of a certain job in 10 days. Salim completes the remaining three fourths of the same job in 20 days. If both Parimal and Salim work together from the beginning, in how many days can they finish the entire job?

Introduction / Context:
This problem tests understanding of individual work rates and combined work rates for two workers. Parimal and Salim complete different fractions of the same job in different times. We first determine their individual efficiencies and then combine them to find how quickly they can finish the job if they start together. Time and work questions of this type are very common in aptitude exams.

Given Data / Assumptions:
- Parimal completes one fourth (1/4) of the job in 10 days when working alone.
- Salim completes the remaining three fourths (3/4) of the job in 20 days when working alone.
- Total work is considered as 1 complete job.
- Work rates are constant for both Parimal and Salim.

Concept / Approach:
We first convert the information about partial work into daily work rates for each person. Then we add the two rates to obtain the combined rate when both work together. Finally we divide the total work by the combined rate to find the time required to finish the entire job when they start together.

Step-by-Step Solution:
Step 1: Let total work = 1 unit. Step 2: Parimal does 1/4 of the work in 10 days, so Parimal's rate = (1/4) / 10 = 1/40 per day. Step 3: Salim does 3/4 of the work in 20 days, so Salim's rate = (3/4) / 20 = 3/80 per day. Step 4: Combined rate when both work together = 1/40 + 3/80. Step 5: Convert 1/40 to 2/80, so combined rate = 2/80 + 3/80 = 5/80 = 1/16 per day. Step 6: Time required to complete the full work together = 1 / (1/16) = 16 days.

Verification / Alternative check:
If the combined rate is 1/16 of the job per day, then in 16 days they should finish the entire job. Multiply: 16 * (1/16) = 1, which is the whole job. Also check relative speeds: Salim is faster because his rate 3/80 is more than 1/40 (which is 2/80). This aligns with the fact that Salim completed three times more work than Parimal in only double the time, confirming that the calculation is consistent.

Why Other Options Are Wrong:
Option 8 days: This would require their combined rate to be 1/8 per day, which is much higher than 1/16 and not supported by their individual rates.
Option 24 days: This would imply a combined rate of 1/24 per day, slower than each of them in many cases, which is not logical when they work together.
Option 12 days: This would imply a combined rate of 1/12 per day, which does not match 1/40 + 3/80 on rechecking.

Common Pitfalls:
Learners sometimes mix up the fractions and treat 1/4 and 3/4 as if they correspond to the same time period. Another mistake is averaging times instead of using rates. Always convert the given partial work information into daily rates and then add or subtract those rates as needed.

Final Answer:
Parimal and Salim together can complete the job in 16 days.