Direction: Vivek works ‘p’ hours a day and rests ‘b’ hours a day. This pattern continues for 1 week, with an exactly opposite pattern next week, and so on for six weeks. Every 7th week he has a different pattern. When he works longer than he rests, his wage per hour is 50% mo
Direction: Vivek works ‘p’ hours a day and rests ‘b’ hours a day. This pattern continues for 1 week, with an exactly opposite pattern next week, and so on for six weeks. Every 7th week he has a different pattern. When he works longer than he rests, his wage per hour is 50% more than what he earns per hour when he rests longer than he works. The following are his daily working hours for the weeks numbered 1 to 19. (A week consists of six days and a month consists of 4 weeks)
|
|
1st week |
7th week |
13th week |
19th week |
|
Working hours |
3 |
5 |
6 |
- |
|
Resting hours |
4 |
6 |
4 |
8 |
In 19th week, Vivek works for more number of hours than rests. Find the number of hours for which he worked per day in 19th week, if he earns Rs. 64800 for the 5th month. (He is getting Rs. 300 per hour)
1). 12 hours
2). 11 hours
3). 9 hours
4). 10 hours
1 answers
Suppose Vivek worked ‘x’ hours per day in 19th week, then he must be resting for ‘x’ hours per day in 20th week;
5th month means 17th week to 20th week;
In the 17th week: Vivek works for 6 hours and rests for 4 hours
In the 19th week: Vivek works for ‘x’ hours and rests for 8 hours
? He works longer than he rests, his wage per hour is 50% more than what he earns per hour when he rests longer than he works;
∴ He will get Rs. (300 × 1.5 = 450) per hour for the work.
In the 18th week: Vivek works for 4 hours and rests for 6 hours
In the 20th week: Vivek works for 8 hours and rests for ‘x’ hours
∴ He will get Rs. 300 per hour for the work.
∴ Total payment of 5th month = 450 × 6 × 6 + 450 × x × 6 + 300 × 4 × 6 + 300 × 8 × 6
⇒ 16200 + 2700x + 7200 + 14400 = 64800
⇒ 37800 + 2700x = 64800
⇒ 2700x = 27000
⇒ x = 10
∴ Vivek worked 10 hours per day in 19th week.