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Back to Practice Questions
MathematicsRatio & Proportion
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If 75 words are typed in 3 minutes by a typist, how many words will be typed in 4 hours?

A

5000

B

6000

C

7500

D

9000

Correct Answer

ЁЯУР MA тАв Math Unitary MethodMathematicsRatio & Proportion
Option B

6000

Quick Summary:

Given: A typist types 75 words in 3 minutes. The total time available is 4 hours.

ЁЯУРMAMath SolutionUnitary Method
ЁЯУЛ Given

A typist types 75 words in 3 minutes. The total time available is 4 hours.

ЁЯФв Formula Used

Total┬аWords=(WordsTime┬аin┬аminutes)├ЧTotal┬аTime┬аin┬аminutes\text{Total Words} = \left( \frac{\text{Words}}{\text{Time in minutes}} \right) \times \text{Total Time in minutes}Total┬аWords=(Time┬аin┬аminutesWordsтАЛ)├ЧTotal┬аTime┬аin┬аminutes

тЪб Exam Hall Shortcut / Speed Trick

Calculate words per minute (75/3 = 25) and multiply by total minutes in 4 hours (240). Quick math: 25├Ч240=25├Ч4├Ч60=100├Ч60=600025 \times 240 = 25 \times 4 \times 60 = 100 \times 60 = 600025├Ч240=25├Ч4├Ч60=100├Ч60=6000.

тЪая╕П Common Student Trap / Pitfall

Many students forget to convert hours to minutes and directly multiply 75 words by 4 hours, ignoring the time unit mismatch.

ЁЯУК Diagram / Illustration
Typing Speed Calculation (Unitary Method) 1 Calculate Rate per Minute Rate = 75 words / 3 minutes = 25 words/minute 2 Convert Total Time to Minutes Total Time = 4 hours ├Ч 60 minutes/hour = 240 minutes 3 Calculate Total Output Total Words = 25 words/min ├Ч 240 min = 6000 words 4 Final Result The typist will type 6000 words in 4 hours. Final Answer: 6000 words (Option B)
ЁЯФв Step-by-Step Solution
1

Calculate rate per minute

Determine how many words the typist types in one minute by dividing total words by time in minutes.

R=753=25┬аwords/minuteR = \frac{75}{3} = 25 \text{ words/minute}R=375тАЛ=25┬аwords/minute

2

Convert total time to minutes

Since the rate is in minutes, convert 4 hours into minutes by multiplying by 60.

T=4├Ч60=240┬аminutesT = 4 \times 60 = 240 \text{ minutes}T=4├Ч60=240┬аminutes

3

Calculate total output

Multiply the rate by the total time in minutes to find the total words typed.

W=25├Ч240=6000W = 25 \times 240 = 6000W=25├Ч240=6000

тЬЕ

B is correct because calculating the rate as 25 words per minute and multiplying by 240 minutes yields a total of 6000 words.

Core Concepts Used
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Unitary Method Time and Work Rate Calculation
ЁЯТб EXAM TIP

This concept of rates is foundational for solving pipes and cisterns problems or speed-distance-time problems where unit consistency is mandatory.

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