Sure, let's tackle both questions one by one.
### Question 13
The price of a [tex]$250 item after successive discounts of 20% and 30% is:
First, we calculate the price after the first discount:
1. The original price of the item is $[/tex]250.
2. The first discount is 20%, which means we subtract 20% of [tex]$250 from the original price:
- 20% of $[/tex]250 is [tex]\( 0.20 \times 250 = 50 \)[/tex]
- Therefore, the price after the first discount is [tex]\( 250 - 50 = 200 \)[/tex]
Next, we calculate the price after applying the second discount on the reduced price:
1. The new price after the first discount is [tex]$200.
2. The second discount is 30%, which means we subtract 30% of $[/tex]200 from the new price:
- 30% of [tex]$200 is \( 0.30 \times 200 = 60 \)
- Therefore, the price after the second discount is \( 200 - 60 = 140 \)
Thus, the final price of the item after successive discounts of 20% and 30% is $[/tex]140.
Answer: c) $140
### Question 14
If a laborer works from 7:15 a.m. to 3:45 p.m. with 1 hour off for lunch, his working time equals:
First, we determine the total time span from 7:15 a.m. to 3:45 p.m. without considering the lunch break:
1. From 7:15 a.m. to 12:00 p.m. (noon) is 4 hours and 45 minutes.
2. From 12:00 p.m. to 3:45 p.m. is 3 hours and 45 minutes.
Adding these time periods together:
- The total working period without the lunch break is [tex]\( 4 \text{ hours } 45 \text{ minutes } + 3 \text{ hours } 45 \text{ minutes } \)[/tex]:
- Minutes: [tex]\( 45 \text{ minutes } + 45 \text{ minutes } = 90 \text{ minutes} = 1 \text{ hour } 30 \text{ minutes } \)[/tex].
- Hours: [tex]\( 4 \text{ hours } + 3 \text{ hours } = 7 \text{ hours } \)[/tex].
- Therefore, [tex]\( 7 \text{ hours } + 1 \text{ hour } 30 \text{ minutes } = 8 \text{ hours } 30 \text{ minutes} \)[/tex].
Next, we consider the 1-hour lunch break:
1. Subtract 1 hour from 8 hours and 30 minutes:
- This leaves us with [tex]\( 7 \text{ hours } 30 \text{ minutes } \)[/tex].
Therefore, the laborer's working time equals 7 hours and 30 minutes.
Answer: 7 hours and 30 minutes.
