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?
A
12:32 PM
B
12:48 PM
C
1:04 PM
D
1:20 PM
Correct Answer:
B. 12:48 PM
Explanation:
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.
A
24 and 36
B
36 and 48
C
48 and 60
D
60 and 72
Correct Answer:
C. 48 and 60
Explanation:
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?
A
1/10
B
1/15
C
1/20
D
1/25
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?
A
7.2 days
B
7.5 days
C
8 days
D
8.5 days
Correct Answer:
A. 7.2 days
Explanation:
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?
A
2 days
B
3 days
C
4 days
D
5 days
Correct Answer:
C. 4 days
Explanation:
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?
A
5 days
B
6 days
C
7 days
D
8 days
Correct Answer:
A. 5 days
Explanation:
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?
A
5 days
B
10 days
C
15 days
D
20 days
Correct Answer:
B. 10 days
Explanation:
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
