What is the number of hours required by raju to complete the job alone?---Here is the extracted content from the image:
**Question 1:**
**Question Stem:**
Varun and Raju, working together, can complete a job in 40 hours whereas Varun alone can complete the same job in 50 hours. The number of hours required by Raju to complete the job alone is:
**Options:**
1. [Content mostly cut off, only "1." is clearly visible at the start of an option line]
**Other Relevant Text:**
* A timestamp "18:46" is visible in the top right corner of the image, likely a system UI element.
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We have a work rate problem. Varun and Raju working together can complete a job in 40 hours. We know that Varun alone can complete the same job in 50 hours. We need to find how many hours Raju requires to complete the job alone.
To solve work rate problems, we use the concept that work rate equals one divided by time taken. If someone completes a job in T hours, their rate is one over T jobs per hour. Varun's rate is one-fiftieth jobs per hour, and the combined rate of both workers is one-fortieth jobs per hour.
Now we set up the mathematical equation. The key principle is that individual work rates add up to the combined work rate. So Varun's rate plus Raju's rate equals their combined rate. This gives us the equation: one-fiftieth plus one over R equals one-fortieth, where R is Raju's unknown time.
Let's solve the equation step by step. Starting with one-fiftieth plus one over R equals one-fortieth, we isolate one over R by subtracting one-fiftieth from both sides. This gives us one over R equals one-fortieth minus one-fiftieth. Finding a common denominator of 200, we get five over 200 minus four over 200, which equals one over 200. Therefore, R equals 200 hours.
Let's verify our answer. Varun's rate of one-fiftieth plus Raju's rate of one over 200 should equal their combined rate of one-fortieth. Converting to a common denominator: four over 200 plus one over 200 equals five over 200, which simplifies to one-fortieth. This confirms our answer is correct. Therefore, Raju requires 200 hours to complete the job alone.