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Ramu, Hari and Sanjay are three typists, who working simultaneously, can type 228 pages in four hours. In one hour, Sanjay can type as many pages more than Hari as Hari can type more than Ramu. During a period of five hours, Sanjay can type as many passages as Ramu 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
- e)16, 19, 22
Correct answer is option 'E'. Can you explain this answer?
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Ramu, Hari and Sanjay are three typists, who working simultaneously, c...
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Ramu, Hari and Sanjay are three typists, who working simultaneously, c...
Given information:
- Ramu, Hari, and Sanjay can type 228 pages in four hours.
- Sanjay's typing speed > Hari's typing speed > Ramu's typing speed.
- In one hour, Sanjay can type as many pages more than Hari as Hari can type more than Ramu.
- In 5 hours, Sanjay can type as many pages as Ramu can in 7 hours.
To find:
- Pages typed per hour by each typist.
Solution:
Let's assume that Ramu, Hari, and Sanjay can type x, y, and z pages per hour respectively.
From the given information, we can form the following equations:
Equation 1: x + y + z = 57 pages/hour (as they can type 228 pages in 4 hours)
Equation 2: z - y = y - x
Simplifying equation 2, we get:
Equation 3: 2y = z + x
From the given information, we can also form the following equation:
Equation 4: 5z = 7x
Solving equations 1 to 4 simultaneously, we get:
x = 16 pages/hour
y = 19 pages/hour
z = 22 pages/hour
Therefore, Ramu types 16 pages per hour, Hari types 19 pages per hour, and Sanjay types 22 pages per hour.
Hence, the correct answer is option (e) 16, 19, 22.
- Ramu, Hari, and Sanjay can type 228 pages in four hours.
- Sanjay's typing speed > Hari's typing speed > Ramu's typing speed.
- In one hour, Sanjay can type as many pages more than Hari as Hari can type more than Ramu.
- In 5 hours, Sanjay can type as many pages as Ramu can in 7 hours.
To find:
- Pages typed per hour by each typist.
Solution:
Let's assume that Ramu, Hari, and Sanjay can type x, y, and z pages per hour respectively.
From the given information, we can form the following equations:
Equation 1: x + y + z = 57 pages/hour (as they can type 228 pages in 4 hours)
Equation 2: z - y = y - x
Simplifying equation 2, we get:
Equation 3: 2y = z + x
From the given information, we can also form the following equation:
Equation 4: 5z = 7x
Solving equations 1 to 4 simultaneously, we get:
x = 16 pages/hour
y = 19 pages/hour
z = 22 pages/hour
Therefore, Ramu types 16 pages per hour, Hari types 19 pages per hour, and Sanjay types 22 pages per hour.
Hence, the correct answer is option (e) 16, 19, 22.
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Community Answer
Ramu, Hari and Sanjay are three typists, who working simultaneously, c...
Let Rohit, Harsh and Sanjeev can type x, y and z pages respectively in 1 h. Therefore, they together can type 4(x + y + z) pages in 4 h
∴ 4(x + y + z) = 228
⇒ x + y + z = 57 …..(i)
Also, z – y = y – x
i.e., 2y = x + z ……(ii)
5z = 7x ……(iii)
From Eqs. (i) and (ii), we get
3y = 57
⇒ y = 19
From Eq. (ii), x + z = 38
x = 16 and z = 22
∴ 4(x + y + z) = 228
⇒ x + y + z = 57 …..(i)
Also, z – y = y – x
i.e., 2y = x + z ……(ii)
5z = 7x ……(iii)
From Eqs. (i) and (ii), we get
3y = 57
⇒ y = 19
From Eq. (ii), x + z = 38
x = 16 and z = 22
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Ramu, Hari and Sanjay are three typists, who working simultaneously, can type 228 pages in four hours. In one hour, Sanjay can type as many pages more than Hari as Hari can type more than Ramu. During a period of five hours, Sanjay can type as many passages as Ramu can, during seven hours. How many pages does each of them type per hour?a)16, 18, 22b)14, 17, 20c)15, 17, 22d)15, 18, 21e)16, 19, 22Correct answer is option 'E'. Can you explain this answer?
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