Time and Work
- 36 men together can build a wall 140 m long in 21 days. The number of men working at the same rate required to build the same wall in 14 days is
-
View Hint View Answer Discuss in Forum
Here, the length of wall is
same in both cases.
∴ M1D1 = M2D2
⇒ 36 × 21 = M2 × 14⇒ M2 = 36 × 21 = 54 days 14 Correct Option: A
Here, the length of wall is
same in both cases.
∴ M1D1 = M2D2
⇒ 36 × 21 = M2 × 14⇒ M2 = 36 × 21 = 54 days 14
- The four walls and ceiling of a room of length 25 m, breadth 12 m and height 10 m are to be painted. Painter A can paint 200 m2 in 5 days, Painter B can paint 250 m2 in 2 days. If A and B work together, they will finish the job in
-
View Hint View Answer Discuss in Forum
Area of the four walls and ceiling of the room
= 2h (l + b) + lb
= 2 × 10 (25 + 12) + 25 × 12
= (20 × 37 + 300) sq. metre
= (740 + 300) sq. metre
= 1040 sq. metre
Area painted by A in 1 day= 200 = 40 sq. metre 5
Area painted by B in 1 day= 250 = 125 sq. metre 2
Area painted by both in1 day
= (125 + 40) sq. metre
= 165 sq. metre∴ Required time = 1040 165 = 208 = 6 10 days 33 33 Correct Option: B
Area of the four walls and ceiling of the room
= 2h (l + b) + lb
= 2 × 10 (25 + 12) + 25 × 12
= (20 × 37 + 300) sq. metre
= (740 + 300) sq. metre
= 1040 sq. metre
Area painted by A in 1 day= 200 = 40 sq. metre 5
Area painted by B in 1 day= 250 = 125 sq. metre 2
Area painted by both in1 day
= (125 + 40) sq. metre
= 165 sq. metre∴ Required time = 1040 165 = 208 = 6 10 days 33 33
- 20 men working 8 hours per day can complete a piece of work in 21 days. How many hours per day must 48 men work to complete the same job in 7 days?
-
View Hint View Answer Discuss in Forum
⇒ 48 × 7 × x = 20 × 21 × 8⇒ x = 20 × 21 × 8 = 10 days 48 × 7 Correct Option: C
⇒ 48 × 7 × x = 20 × 21 × 8⇒ x = 20 × 21 × 8 = 10 days 48 × 7
- A group of workers can complete a piece of work in 50 days, when they are working individually. On the first day one person works, on the second day another person joins him, on the third day one more person joins them and this process continues till the work is completed.
How many approximate days are needed to complete the work?
-
View Hint View Answer Discuss in Forum
Let the work be finished in x days.
x + x - 1 + x - 2 + ..... + 1 = 1 50 50 50 50
⇒ x + x – 1 + x – 2 + .... + 1 = 50
i.e., 10 + 9 + 8 + .... + 1 = 55
9 + 8 + .... + 1 = 45
∴ Required time = 10 daysCorrect Option: C
Let the work be finished in x days.
x + x - 1 + x - 2 + ..... + 1 = 1 50 50 50 50
⇒ x + x – 1 + x – 2 + .... + 1 = 50
i.e., 10 + 9 + 8 + .... + 1 = 55
9 + 8 + .... + 1 = 45
∴ Required time = 10 days
- Work done by (x + 4) men in (x + 5) days is equal to the work done by (x – 5) men in (x + 20) days. Then the value of x is
-
View Hint View Answer Discuss in Forum
Using Rule 1,
According to the question,
M1D1 = M2D2
⇒ (x + 4) (x + 5)
= (x – 5) (x + 20)
⇒ x2 + 5x + 4x + 20
= x2 – 5x + 20x – 100
⇒ 9x + 20 = 15x – 100
⇒ 15x – 9x = 100 + 20
⇒ 6x = 120⇒ x = 120 = 20 6 Correct Option: A
Using Rule 1,
According to the question,
M1D1 = M2D2
⇒ (x + 4) (x + 5)
= (x – 5) (x + 20)
⇒ x2 + 5x + 4x + 20
= x2 – 5x + 20x – 100
⇒ 9x + 20 = 15x – 100
⇒ 15x – 9x = 100 + 20
⇒ 6x = 120⇒ x = 120 = 20 6
