Arithmetic - Time & Work - Previous Year CAT/MBA Questions
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In Bilaspur village, 12 men and 18 boys completed construction of a primary health center in 60 days, by working for 7.5 hours a day. Subsequently the residents of the neighbouring Harigarh village also decided to construct a primary health center in their locality, which would be twice the size of the facility build in Bilaspur. If a man is able to perform the work equal to the same done by 2 boys, then how many boys will be required to help 21 men to complete the work in Harigarh in 50 days, working 9 hours a day?
- (a)
45 boys
- (b)
48 boys
- (c)
40 boys
- (d)
42 boys
Answer: Option D
Text Explanation :
A man is able to perform the work equal to the same done by 2 boys.
∴ 18 boys ≡ 9 men
Work done by 12 men and 18 boys, working 7.5 hours a day, in 60 days = (12 + 9) × 7.5 × 60
= 21 × 7.5 × 60 man hours
As the facility in Harigarh is twice that in Bilaspur, man hours required to build health facility in Harigarh
= 2 × 21 × 7.5 × 60
Let a boys be required to complete the work in 50 days, working 9 hours a day.
∴ we have,
(21 + a/2) × 9 × 50 = 2 × 21 × 7.5 × 60
∴ a = 42
Hence, option (d).
Workspace:
A contract is to be completed in 56 days and 104 men are set to work, each working 8 hours a day. After 30 days, 2/5th of the work is finished. How many additional men may be employed so that work may be completed on time, each man now working 9 hours per day?
- (a)
56 men
- (b)
65 men
- (c)
46 men
- (d)
None of the above
Answer: Option A
Text Explanation :
Work done by 104 men, working 8 hours a day, in 30 days = 104 × 8 × 30 man hours.
This is 2/5th of the total work.
= 104 × 8 × 30 × × = 104 × 4 × 90 man hours.
∴ Remaining work, which is 3/5th of the total work
Let a more men be employed to complete this work.
∴ (104 + a) × 9 × (56 – 30) = 104 × 4 × 90
∴ a = 56
Hence, option (a).
Workspace:
Three Professors Dr. Gupta, Dr. Sharma and Dr. Singh are evaluating answer scripts of a subject. Dr. Gupta is 40% more efficient than Dr. Sharma, who is 20% more efficient than Dr. Singh. Dr. Gupta takes 10 days less than Dr. Sharma to complete the evaluation work. Dr. Gupta starts the evaluation work and works for 10 days and then Dr. Sharma takes over. Dr. Sharma evaluates for next 15 days and then stops. In how many days, Dr. Singh can complete the remaining evaluation work.
- (a)
7.2 days
- (b)
9.5 days
- (c)
11.5 days
- (d)
None of these
Answer: Option A
Text Explanation :
Let Dr. Gupta take x days to complete the evaluation work.
∴ Dr. Sharma takes x + 10 days
As Dr. Gupta is 40% more efficient than Dr. Sharma, we have
=
∴ x = 25
∴ x + 10 = 35
Also, Dr. Sharma is 20% more efficient than Dr. Singh.
∴ If Dr. Singh takes y days to complete the evaluation work,
=
∴ y = 42
Now, let Dr. Singh complete the evaluation work in n days after Dr. Gupta has worked for 10 days and Dr. Sharma has worked for 15 days.
∴ + + = 1
∴ n = 7.2
Hence, option (a).
Workspace:
Three pipes A, B and C are connected to a tank. These pipes can fill the tank separately in 5 hours, 10 hours and 15 hours respectively. When all the three pipes were opened simultaneously, it was observed that pipes A and B were supplying water at 3/4th of their normal rates for the first hour after which they supplied water at the normal rate. Pipe C supplied water at 2/3rd of its normal rate for first 2 hours, after which it supplied at its normal rate. In how much time, tank would be filled.
- (a)
1.05 Hours
- (b)
2.05 Hours
- (c)
3.05 Hours
- (d)
None of these
Answer: Option C
Text Explanation :
Let the pipes work for n hours.
By the given conditions,
+ + (n - 1) + + = 1
∴ + + (n - 1) + + = 1
∴ + + + = 1
∴ + = 1 - -
∴ =
∴ 11n - 13 =
∴ n ≈ 3.05
Hence, option (c).
Workspace:
Because of economic slowdown, a multinational company curtailed some of the allowances of its employees. Rashid, the marketing manager of the company whose monthly salary has been reduced to Rs.42000 is unable to cut down his expenditure. He finds that there is a deficit of Rs.2000 between his earnings and expenses in the first month. This deficit, because of inflationary pressure, will keep on increasing by Rs.500 every month. Rashid has a saving of Rs.60000 which will be used to fill this deficit. After his savings get exhausted, Rashid would start borrowing from his friends. How soon will he start borrowing?
- (a)
10th month
- (b)
11th month
- (c)
12th month
- (d)
13th month
Answer: Option D
Text Explanation :
If Rashid’s savings fill his deficit for n months,
60000 = [4000 + (n - 1)500]
∴ n2 + 7n - 240 = 0
∴ n ≈ 12.38
∴ Rashid savings last for 12 months, after which he has to start borrowing from the 13th month.
Hence, option (d).
Workspace:
Aditya, Vedus and Yuvraj alone can do a job in 6 weeks, 9 weeks and 12 weeks respectively. They work together for 2 weeks. Then Aditya leaves the job. Vedus leaves the job a week earlier to the completion of the work. The job would be completed in:
- (a)
4 weeks
- (b)
5 weeks
- (c)
7 weeks
- (d)
None of the above
Answer: Option A
Text Explanation :
Aditya, Vedus and Yuvraj do (1/6), (1/9) and (1/12) of the work respectively in a week. Let the total time taken to complete the work be n weeks.
Then,
2 + (n - 1) + n = 1
∴ = 1
∴ n = 4
Hence, option (a).
Workspace:
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