Answer :
To find out when Riaz and Razi will first finish marking a paper at the same time, we need to determine the least common multiple (LCM) of their individual marking times. Here’s a step-by-step approach to solve this problem:
1. Determine the marking times:
- Riaz takes 30 minutes to mark a paper.
- Razi takes 25 minutes to mark a paper.
2. Find the LCM of the marking times:
- The least common multiple (LCM) of 30 and 25 would give us the smallest amount of time after which both Riaz and Razi will finish marking papers at the same moment.
3. Calculate the LCM:
- To find the LCM, we can use the formula:
[tex]\[ \text{LCM}(a, b) = \frac{|a \times b|}{\text{GCD}(a, b)} \][/tex]
- Here \( a = 30 \) and \( b = 25 \).
4. Find the GCD of 30 and 25:
- The greatest common divisor (GCD) of 30 and 25 is 5.
5. Calculate the LCM using the GCD:
- Substitute the values into the LCM formula:
[tex]\[ \text{LCM}(30, 25) = \frac{30 \times 25}{\text{GCD}(30, 25)} = \frac{750}{5} = 150 \text{ minutes} \][/tex]
6. Find the finishing time:
- Both start marking papers at 11:00 AM.
- Add 150 minutes to the starting time of 11:00 AM.
7. Conversion to appropriate time format:
- 150 minutes is equal to 2 hours and 30 minutes.
- Adding 2 hours and 30 minutes to 11:00 AM results in:
[tex]\[ 11:00 \text{ AM} + 2 \text{ hours and } 30 \text{ minutes} = 1:30 \text{ PM} \][/tex]
Thus, the first time Riaz and Razi will both finish marking a paper at the same time is at:
[tex]\[ \boxed{1:30 \text{ PM}} \][/tex]
So, the correct answer is:
c) 1:30
1. Determine the marking times:
- Riaz takes 30 minutes to mark a paper.
- Razi takes 25 minutes to mark a paper.
2. Find the LCM of the marking times:
- The least common multiple (LCM) of 30 and 25 would give us the smallest amount of time after which both Riaz and Razi will finish marking papers at the same moment.
3. Calculate the LCM:
- To find the LCM, we can use the formula:
[tex]\[ \text{LCM}(a, b) = \frac{|a \times b|}{\text{GCD}(a, b)} \][/tex]
- Here \( a = 30 \) and \( b = 25 \).
4. Find the GCD of 30 and 25:
- The greatest common divisor (GCD) of 30 and 25 is 5.
5. Calculate the LCM using the GCD:
- Substitute the values into the LCM formula:
[tex]\[ \text{LCM}(30, 25) = \frac{30 \times 25}{\text{GCD}(30, 25)} = \frac{750}{5} = 150 \text{ minutes} \][/tex]
6. Find the finishing time:
- Both start marking papers at 11:00 AM.
- Add 150 minutes to the starting time of 11:00 AM.
7. Conversion to appropriate time format:
- 150 minutes is equal to 2 hours and 30 minutes.
- Adding 2 hours and 30 minutes to 11:00 AM results in:
[tex]\[ 11:00 \text{ AM} + 2 \text{ hours and } 30 \text{ minutes} = 1:30 \text{ PM} \][/tex]
Thus, the first time Riaz and Razi will both finish marking a paper at the same time is at:
[tex]\[ \boxed{1:30 \text{ PM}} \][/tex]
So, the correct answer is:
c) 1:30
