 Important for :
1
The hourly wages of a mason have increased by 25%. Since the increase, the number of hours he works daily has reduced by 16%. If he was earning Rs. 120 per day before the increase, how much (in Rs.) is he earning now?
» Explain it
C
Daily wages = hourly wages × work hours.

Let the original hourly wages and work hours be Rs. x and y hours respectively.

Since he used to earn Rs. 120 earlier, xy = 120

New hourly wages = Rs. (1.25x) and new working hours = 0.84y

New daily wages = (1.25x)(0.84y) = 1.05xy = 1.05 × 120 = Rs. 126

Hence, option C is correct.
2
Radhe does 70% of some work in 15 days. Later, with Shyam’s help, she completes the remaining work in 4 days. In how many days can Shyam alone complete the entire work?
» Explain it
C
Let total work = 150 units

Since Radhe does 70% of the work (i.e. 105 units) in 15 days,

 Radhe = 105 = 7 units per day 15

Work left = 150 − 105 = 45 units

Let Shyam do x units of work per day. Shyam and Radhe finish the pending work in 4 days.

∴   4(x + 7) = 45

∴   4x = 45 − 28 = 17 i.e. x = 4.25 units

∴   Time taken by Shyam to complete the work = 150/4.25 = 35.29 ≈ 35.3 days

Note that 0.3 is equivalent to 5/17 (among the options).

Hence, option C is correct.
3
A and B undertake a project worth Rs. 54000 . A alone can do the work in 10 days. They work together for 3 days. After 3 days, B works alone for 3 days and A completes the remaining work in 3 more days.What is the share of B in the earnings?
» Explain it
A
A can do 10% work in a day. A has worked 6 days in total. And so has B

A completed 60% work in 6 days and B did 40% in 6 days.

Efficiency of A and B = 6 : 4

 B's share = 4 × 54000 = 21600 10

Hence, option A is correct.
4
If the ratio of speed of doing work of three persons is 1 : 3 : 5, what is the ratio of time taken by these people to do the same amount of work?
» Explain it
D
Let the speed of doing work of the three persons be 1x, 3x and 5x respectively

Time taken by each person = amount of work done/speed of doing work

Let the amount of work for each person = y (∵ work done is same)

 The time taken by the first person = y x

 The time taken by the second person = y 3x

 The time taken by the third person = y 5x

 The ratio of time taken = y : y : y x 3x 5x

 ⇒ 1 : 1 : 1 = 15 : 5 : 3 3 5

Hence, option D is correct.
5
It takes 6 workers a total of 10 hours to assemble a computer, with each working at the same rate. If six workers start at 9.00 am, and one worker per hour is added beginning at 3.00 pm, at what time will the computer assembled?
» Explain it
C
6 workers complete some work in 10 hours.

1 worker completes the same work in 60 hours.

Let the total work be equivalent to 60 man-hours.

From 9.00 am to 3.00 pm, all 6 workers work together for 6 hours.

Amount of work done by 6 workers in 6 hours is 6 × 6 = 36 man-hours

From 3.00 pm to 4.00 pm, 7 man-hours of work will be done.

From 4.00 pm to 5.00 pm, 8 man-hours of work will be done.

From 5.00 pm to 6.00 pm, 9 man-hours of work will be done.

Thus, total amount of work done up to 6.00 pm is 36 + 7 + 8 + 9 = 60 man-hours

Thus, the computer will be assembled at 6.00 pm.

Hence, option C is correct.