Question

Rohit, Harsha and Sanjeev are three typists who, working simultaneously, can type 216 pages in four hours. In one hour, Sanjeev can type as many pages more than Harsha as Harsha can type more than Rohit. During a period of five hours, Sanjeev can type as many pages as Rohit can during seven hours How many pages does each of them type per hour?

• A. 16, 18, 22
• B. 14, 17, 20
• C. 15, 17, 22
• D. 15, 18, 21

Answer 1

The Correct Option is D

The correct option is (D): 15, 18, 21
Explanation: To solve the problem, let's denote the number of pages typed per hour by Rohit, Harsha, and Sanjeev as \( R \), \( H \), and \( S \) respectively.
1. From the information given, the three of them together can type 216 pages in 4 hours. Thus:
\[R + H + S = \frac{216}{4} = 54\]
2. It's also stated that in one hour, Sanjeev can type as many pages more than Harsha as Harsha can type more than Rohit. This can be expressed as:
\[S - H = H - R \quad \Rightarrow \quad S = 2H - R\]
3. Additionally, during a period of five hours, Sanjeev can type as many pages as Rohit can during seven hours:
\[5S = 7R \quad \Rightarrow \quad S = \frac{7}{5}R\]
Now we have three equations:
1. \( R + H + S = 54 \)
2. \( S = 2H - R \)
3. \( S = \frac{7}{5}R \)
Substituting \( S \) from the third equation into the first two:
1. \( R + H + \frac{7}{5}R = 54 \)
 \[\Rightarrow \quad \frac{12}{5}R + H = 54 \quad \Rightarrow \quad H = 54 - \frac{12}{5}R\]
2. Now substitute \( S \) into the second equation:
\[\frac{7}{5}R = 2H - R\]
Rearranging gives:
\[ \frac{7}{5}R + R = 2H \quad \Rightarrow \quad \frac{12}{5}R = 2H \quad \Rightarrow \quad H = \frac{6}{5}R\]
Substituting \( H \) back into \( H = 54 - \frac{12}{5}R \):
\[\frac{6}{5}R = 54 - \frac{12}{5}R\]
Multiplying everything by 5 to eliminate the fraction:
\[6R = 270 - 12R \quad \Rightarrow \quad 18R = 270 \quad \Rightarrow \quad R = 15\]
Now, substituting \( R \) back to find \( H \) and \( S \):
\[H = \frac{6}{5} \times 15 = 18\]
\[S = \frac{7}{5} \times 15 = 21\]
Thus, the pages typed per hour by Rohit, Harsha, and Sanjeev are:
- Rohit: 15 pages
- Harsha: 18 pages
- Sanjeev: 21 pages
Therefore, the answer is Option D: 15, 18, 21.