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Arithmetic: Time and Work Test-6
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Question 1 |
8 men can complete a piece of work.in 20 days. 8 women can complete the same work in 32 days. In how many days will 5 men and 8 women together complete the same work?
16 days | |
12 days | |
14 days | |
10 days |
Question 1 Explanation:
Let the amount of work be 320 units.
8 men do 1280 units of work in 20 days.
1 man can do 160 units of work in 20 days.
Therefore, 1 man can of 8 units of work per day.
Similarly, 1 woman can do {1280/(32 x 5)} = 5 units of work per day.
Therefore 5 men+ 8 women can do {(5 x 8) + (8X5)} = 80 units of work per day.
The number of days required to complete the work is$ \frac{1280}{80}=16days$
8 men do 1280 units of work in 20 days.
1 man can do 160 units of work in 20 days.
Therefore, 1 man can of 8 units of work per day.
Similarly, 1 woman can do {1280/(32 x 5)} = 5 units of work per day.
Therefore 5 men+ 8 women can do {(5 x 8) + (8X5)} = 80 units of work per day.
The number of days required to complete the work is$ \frac{1280}{80}=16days$
Question 2 |
M and N can do a work in 10 days and 15 days respectively. If M starts on the work and both work alternately day after day, in how many days will the work be completed?
10 | |
12 | |
8 | |
9 |
Question 2 Explanation:
Let the total work be = 30 units.
M does work at 30/10 = 3 units/day.
N does work at 30/15 = 2 units/day.
If they work alternatively, the total work finished in 2 days is 3+2= 5 units.
They can finish the work in 30/5 = 6 days working in pairs .
Total days required = 6 x 2 = 12 days.
M does work at 30/10 = 3 units/day.
N does work at 30/15 = 2 units/day.
If they work alternatively, the total work finished in 2 days is 3+2= 5 units.
They can finish the work in 30/5 = 6 days working in pairs .
Total days required = 6 x 2 = 12 days.
Question 3 |
3 men can complete a piece of work in 6 days. 5 women can complete the same work in 18 days. In how many days will 4 men and 10womentogether complete the same work?
3 days | |
5 days | |
2 days | |
days |
Question 3 Explanation:
Let the work be 180 units.
3 men do 180 units in 6 days.
1 man can do 180/(6 x 3) = 10 units in 1 day.
4 men in 1 day do 40 units of work.
5 women can complete 180 units of work in 18 days.
In 1 day 1 woman does {180/(18 x 5)} = 2 units of work.
10 women in 1 day do 20 units of work.
Total per day = 40+20 = 60 units of work.
The work can be finished in 180 /60 = 3 days.
3 men do 180 units in 6 days.
1 man can do 180/(6 x 3) = 10 units in 1 day.
4 men in 1 day do 40 units of work.
5 women can complete 180 units of work in 18 days.
In 1 day 1 woman does {180/(18 x 5)} = 2 units of work.
10 women in 1 day do 20 units of work.
Total per day = 40+20 = 60 units of work.
The work can be finished in 180 /60 = 3 days.
Question 4 |
A and B can finish a job in 10 days while Band C can do it in 18 days. A started the job worked for 5 days, then B worked for 10 days and the remaining job was finished by C in 15 days. In how many days could C alone have finished the whole job?
30 days | |
15 days | |
45 days | |
24 days |
Question 4 Explanation:
15C+10(10-C)+5(8+C) = 180,
=> 15C+100-10C+40+5C = 180
=> 10 C = 40
=> C= 4 units per day.
C can finish the work in 180/4 =45 days.
Question 5 |
Aman's basic pay for a 40 hours week is Rs.200. Overtime is paid at 25% above the basic rate. In a certain week, he worked overtime and his total was Rs.300. He therefore, worked for a total of (in hours):
52 | |
56 | |
58 | |
62 |
Question 5 Explanation:
For normal work he received 200/40 = Rs. 5 per hour.
If he received 25 % more then he receives = 5 x 5/4 = Rs. 6.25 per hour.
He received a total of 300.
Let him work on extra wage for x days.
Therefore, 200 + 6.25x= 300,
x= {(100 x 4)/(5 x 5)}= 16 days.
Aman worked for total 40+16 = 56 days.
If he received 25 % more then he receives = 5 x 5/4 = Rs. 6.25 per hour.
He received a total of 300.
Let him work on extra wage for x days.
Therefore, 200 + 6.25x= 300,
x= {(100 x 4)/(5 x 5)}= 16 days.
Aman worked for total 40+16 = 56 days.
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