M4maths Previous Puzzles

08 Mar 2022 Time and Work

On 1st Feb 2022, Priya and Rakhi signed a contract of a work with a firm for Rs. 10,000 and started working immediately together for 8 hours per day. On 28th Feb 2022 they finished the work and the share of Priya was Rs. 1000 more than that of Rakhi. If Priya had worked alone for the same hours per day then on which date of the year 2022, she would have finished the work?

OPtion

1) 22nd March
2) 3rd April
3) 25th March
4) 6th April
5) 28th March
6) 4th April
7) 23rd March
8) 20th March
9) 24th March
10) None of these

Solution

Let the share of Priya=x and Rakhi=x-1000
So, x + (x-1000) = 10000
x = 5500
.'. Ratio of shares of Priya and Rakhi = 5500 : 4500 = 11 : 9
We know that share is directly proportional to efficiency
=> Priya completed 11/20 and Rakhi 9/20 of the total work in 28 days.
Hence, working alone Priya will take 28*20/11 = 50.9 days
Therefor, Priya alone can finish the work in 28 days of Feb + 22.9 days of March
So on 23rd March she will finish the work.

Correct Option: 7 Best Solution (3)

Pargat Pal Singh   3 years AGO

Ratio of efficiency of priya and Rakhi=5500:4500=11:9
If 20 units of work is completed together on each day, total work =28x20=560 units
Days taken by Priya alone to complete work =560/11=50.9090... days i.e completed on 23rd March

Like? Yes (3) | No   

Mayank Kandoi   3 years AGO

Total work = 28*8 = 224 hours

Money breakup,
Priya : Rakhi :: 5500 : 4500
This means Priya worked 5500/10000 (=11/20) times of total hours

For Priya,
Total work = 224*11/20 = 123.2 hours
Work per day = 123.2 / 28 = 4.4 hours
Remaining work = 224 - 123.2 = 100.8
Extra days required = 100.8 / 4.4 = 22.9

Option 7

Like? Yes (2) | No (1)  

Varun   3 years AGO

Priya's share is 1k more = Let x+1k
=> x+x+1k = 10k
So x = 4.5k
So work hours will be accordingly
5.5 : 4.5 for Priya and Rakhi
i.e. out of 8 = 5.5/10 * 8 = 4.4 hours a day
If she had worked on it alone, then she would have to finish total work of 8 * 28 = 224
So days needed = 224/4.4 = 50.9 = 51
=> 28 + (51-28) days = 28 + 23 days
So would have completed on 23rd March

Like? Yes (1) | No