Showing 141–150 of 1,106 questions
What is the HCF of 100, 150, and 200?
Explanation:
100 = 2² × 5², 150 = 2 × 3 × 5², 200 = 2³ × 5².
Common factors: 2¹ × 5² = 2 × 25 = 50.
Find the LCM of 84 and 140.
Explanation:
This question asks us to find the least common multiple (LCM) of two numbers using prime factorization.
Step 1: Find prime factorization of 84
Break 84 into its prime factors by dividing by smallest primes.
\[84 = 2^2 \times 3 \times 7\]
Step 2: Find prime factorization of 140
Break 140 into its prime factors by dividing by smallest primes.
\[140 = 2^2 \times 5 \times 7\]
Step 3: Calculate LCM using highest powers of all prime factors
LCM is found by taking the highest power of each prime factor that appears in either number.
\[\text{LCM} = 2^2 \times 3 \times 5 \times 7 = 4 \times 3 \times 5 \times 7 = 420\]
The LCM of 84 and 140 is 420, which is option (A).
Three bells ring at intervals of 8, 12, and 16 minutes. If they ring together at 12:00 PM, at what time will they ring together again?
A12:32 PM
B12:48 PM
C1:04 PM
D1:20 PM
Correct Answer:
B. 12:48 PMExplanation:
Need to find LCM of 8, 12, 16. 8 = 2³, 12 = 2² × 3, 16 = 2⁴. LCM = 2⁴ × 3 = 48 minutes.
So they ring again at 12:00 + 48 min = 12:48 PM.
The HCF of two numbers is 12, and their LCM is 240. If the difference between the numbers is 12, find the numbers.
A24 and 36
B36 and 48
C48 and 60
D60 and 72
Correct Answer:
C. 48 and 60Explanation:
Let numbers be 12a and 12b where HCF(a,b)=1. LCM = 12ab = 240, so ab = 20.
Numbers: 12a and 12b with |12a - 12b| = 12, so |a - b| = 1.
If a=4, b=5: numbers are 48 and 60.
Check: 48-60 = -12 (difference is 12).
A can complete a work in 20 days. How much work will A complete in 5 days?
Explanation:
This question tests the concept of work rate and how much work is completed in a given time period.
Step 1: Find A's work rate per day
A completes the entire work in 20 days, so the work rate is 1 part per day.
\[\text{Work rate} = \frac{1}{20} \text{ work per day}\]
Step 2: Calculate work completed in 5 days
Multiply the daily work rate by the number of days.
\[\text{Work completed} = \frac{1}{20} \times 5 = \frac{5}{20}\]
Step 3: Simplify the fraction
Reduce the fraction to its simplest form by dividing both numerator and denominator by 5.
\[\frac{5}{20} = \frac{1}{4}\]
A will complete 1/4 of the work in 5 days.
B can do a job in 15 days. What is B's work rate per day?
Explanation:
This question asks us to find B's daily work rate when the total job can be completed in 15 days.
Step 1: Understand work rate definition
Work rate is the fraction of total work completed per day.
\[\text{Work Rate} = \frac{\text{Total Work}}{\text{Total Days}}\]
Step 2: Define total work as 1 complete job
Since B completes the entire job, the total work equals 1.
\[\text{Total Work} = 1\]
Step 3: Calculate B's daily work rate
B completes the job in 15 days, so divide the work by the number of days.
\[\text{B's Work Rate} = \frac{1}{15} \text{ per day}\]
B's work rate is 1/15 of the job per day, which means B completes one-fifteenth of the job each day for 15 days to finish it completely.
Q.147
Medium
Time and Work
A can complete a work in 12 days and B can complete it in 18 days. How many days will they take working together?
A7.2 days
B7.5 days
C8 days
D8.5 days
Correct Answer:
A. 7.2 daysExplanation:
A's rate = 1/12, B's rate = 1/18.
Combined rate = 1/12 + 1/18 = 3/36 + 2/36 = 5/36.
Time = 36/5 = 7.2 days
If 5 workers can build a wall in 8 days, how many days will 10 workers take to build the same wall?
A2 days
B3 days
C4 days
D5 days
Correct Answer:
C. 4 daysExplanation:
This question tests the concept of inverse proportionality between the number of workers and the time required to complete a fixed task.
Step 1: Calculate total work in worker-days
Work is constant regardless of the number of workers, so we multiply workers by days.
\[\text{Total Work} = 5 \text{ workers} \times 8 \text{ days} = 40 \text{ worker-days}\]
Step 2: Set up the equation with new number of workers
With 10 workers, the same 40 worker-days of work must be completed.
\[10 \text{ workers} \times d \text{ days} = 40 \text{ worker-days}\]
Step 3: Solve for the number of days
Divide total work by the number of workers to find days required.
\[d = \frac{40}{10} = 4 \text{ days}\]
When 10 workers work together, they will build the same wall in 4 days.
Q.149
Medium
Time and Work
A can do a work in 10 days, B can do it in 15 days, and C can do it in 30 days. How long will they take working together?
A5 days
B6 days
C7 days
D8 days
Correct Answer:
A. 5 daysExplanation:
Combined rate = 1/10 + 1/15 + 1/30 = 3/30 + 2/30 + 1/30 = 6/30 = 1/5.
Time = 5 days
Q.150
Medium
Time and Work
A completes 1/3 of work in 5 days. How many more days will A need to complete the remaining work?
A5 days
B10 days
C15 days
D20 days
Correct Answer:
B. 10 daysExplanation:
A completes 1/3 work in 5 days, so rate = 1/15 per day.
Remaining work = 2/3.
Days needed = (2/3)/(1/15) = (2/3) × 15 = 10 days
