Q1) A builder appoints three construction workers Akash, Sunil and Rakesh on one of his sites. They take 20, 30 and 60 days respectively to do a piece of work. How many days will it take Akash to complete the entire work if he is assisted by Sunil and Rakesh every third day?
A.10 days
B.15 days
C. 25 days
D. 30 days
E. 45 days
Explanation
Answer: B 15 days
Solution:
Total work done by Akash, Sunil and Rakesh in 1 day = {(1/20) + (1/30) + (1/60)} = 1/10
Work done along by Akash in 2 days = (1/20) × 2 = 1/10
Work Done in 3 days (1 day of all three together + 2 days of Akash’s work) = (1/10) + (1/10) = 1/5
So, work done in 3 days = 1/5
Time taken to complete the work = 5×3 = 15 days
Q2) To complete a piece of work, Samir takes 6 days and Tanvir takes 8 days alone respectively. Samir and Tanvir took Rs.2400 to do this work. When Amir joined them, the work was done in 3 days. What amount was paid to Amir?
A. Rs. 300
B. Rs. 400
C. Rs. 800
D. Rs. 500
E. Rs. 100
Explanation
Answer: (A) Rs.300
Solution:
Total work done by Samir and Tanvir = {(1/6) + (1/8)} = 7/24
Work done by Amir in 1 day = (1/3) – (7/24) = 1/24
Amount distributed between each of them = (1/6) : (1/8) : (1/24) = 4:3:1
Amount paid to Amir = (1/24) × 3 × 2400 = Rs.300
Q3) . Dev completed the school project in 20 days. How many days will Arun take to complete the same work if he is 25% more efficient than Dev?
A. 10 days
B. 12 days
C. 16 days
D. 15 days
E. 5 days
Explanation
Answer: (C) 16 days
Solution:
Let the days taken by Arun to complete the work be x
The ratio of time taken by Arun and Dev = 125:100 = 5:4
5:4 :: 20:x
⇒ x = {(4×20) / 5}
⇒ x = 16
Q4) Time taken by A to finish a piece of work is twice the time taken B and thrice the time taken by C. If all three of them work together, it takes them 2 days to complete the entire work. How much work was done by B alone?
A. 2 days
B. 6 days
C. 3 days
D. 5 days
E. Cannot be determined
Explanation
Answer: (B) 6 days
Solution:
Time taken by A = x days
Time taken by B = x/2 days
Time Taken by C = x/3 days
⇒ {(1/x) + (2/x) + (3/x) = 1/2
⇒ 6/x = 1/2
⇒ x = 12
Time taken by B = x/2 = 12/2 = 6 days
Q5) Sonal and Preeti started working on a project and they can complete the project in 30 days. Sonal worked for 16 days and Preeti completed the remaining work in 44 days. How many days would Preeti have taken to complete the entire project all by herself?
A. 20 days
B. 25 days
C. 55 days
D. 46 days
E. 60 days
Explanation
Answer: (E) 60 days
Solution:
Let the work done by Sonal in 1 day be x
Let the work done by Preeti in 1 day be y
Then, x+y = 1/30 ——— (1)
⇒ 16x + 44y = 1 ——— (2)
Solving equation (1) and (2),
x = 1/60
y = 1/60
Thus, Preeti can complete the entire work in 60 days
Q6) Ram and Shyam are standing at two ends of a room with a width of 30 m. They start walking towards each other along the width of the room with a Speed of 2 m/s and 1 m/s, respectively. Find the total distance travelled by Ram when he meets Shyam for the third time.
A. 110 m
B. 112 m
C. 120 m
D. 100 m
E. None
Explanation
Answer (D) 100 m
Solution:
When Ram meets Shyam for the third time, they together would have covered a Distance of 5d, i.e 5x30m = 150 m.
The ratio of Speed of Ram and Shyam = 2:1, so the total distance travelled by them will also be in the ratio 2:1 as the Time taken is constant.
So the Distance travelled by Ram will be 2/3 x 150= 100 m
Q7) A man decided to cover a distance of 6 km in 84 minutes. He decided to cover two thirds of the distance at 4 km / hr and the remaining at some different speed. Find the speed after the two third distance has been covered.
A. 5 kmph
B. 7 kmph
C. 9 kmph
D. 3 kmph
E. None of these
Explanation
Answer (A) 5 kmph
Solution:
We are given that two thirds of the 6 km was covered at 4 km / hr i.e. 4 km distance was covered at 4 km / hr. Time taken to cover 4 km = 4 km / 4 km / hr = 1 hr = 60 minutes
Time left = 84 – 60 = 24 minutes
Now, the man has to cover remaining 2 km in 24 minutes or 24 / 60 = 0.4 hours
Speed required for remaining 2 km = 2 km / 0.4 hr = 5 km / hr
Q8) . While going to office, Ramesh travels at a speed of 30 kmph and on his way back, he travels at a speed of 45 kmph. What is his average speed of the whole journey?
A. 45 kmph
B. 36 kmph
C. 32 kmph
D. 42 kmph
E. E. None of these
Explanation
Answer (B) 36 kmph
Solution:
When distance travelled is same, then average speed = 2ab / (a+b); (where a and b are two different speeds) therefore,
The Average Speed = Therefore, Average Speed = 2 x 45 x 30 / 45 + 30, solving this we get 36 kmph.
Q9) Find the value of 50P2
A. 4500
B. 3260
C. 2450
D. 1470
E. None of these
Explanation
Correct Option: (c)
Q10) How many words can be formed by using letters of the word ‘DELHI’?
A. 50
B. 72
C. 85
D. 120
E. None of these
Explanation
Correct Option: (D)
Hint:
The word ‘DELHI’ contains 5 letters
Therefore, required number of words = 5P5 = 5! = (5 × 4 × 3 × 2 × 1) = 120
120 words can be formed by using letters of the word ‘DELHI’
