Answer :
Alright, let's work through these two problems step-by-step.
### Problem 17:
Question: On increasing the price of an article by 16%, it becomes ₹1479. What was its original price?
Solution:
1. Let the original price of the article be \( x \).
2. Since the price increased by 16%, the new price is \( x + 0.16x = 1.16x \).
3. We are given that after the increase, the price becomes ₹1479.
Thus, we have the equation:
[tex]\[ 1.16x = 1479 \][/tex]
4. To find the original price \( x \), we need to solve for \( x \):
[tex]\[ x = \frac{1479}{1.16} \][/tex]
5. Performing the division, we get:
[tex]\[ x = 1275.0 \][/tex]
So, the original price of the article was ₹1275.
### Problem 18:
Question: Pratibha reduced her weight by 15%. If now she weighs 59.5 kg, what was her earlier weight?
Solution:
1. Let Pratibha's original weight be \( y \).
2. She reduced her weight by 15%, which means she now weighs 85% of her original weight.
This can be written as:
[tex]\[ 0.85y = 59.5 \][/tex]
3. To find the original weight \( y \), we solve for \( y \):
[tex]\[ y = \frac{59.5}{0.85} \][/tex]
4. Performing the division, we get:
[tex]\[ y = 70.0 \][/tex]
So, Pratibha's original weight was 70.0 kg.
In summary:
- The original price of the article was ₹1275.
- Pratibha's original weight was 70.0 kg.
### Problem 17:
Question: On increasing the price of an article by 16%, it becomes ₹1479. What was its original price?
Solution:
1. Let the original price of the article be \( x \).
2. Since the price increased by 16%, the new price is \( x + 0.16x = 1.16x \).
3. We are given that after the increase, the price becomes ₹1479.
Thus, we have the equation:
[tex]\[ 1.16x = 1479 \][/tex]
4. To find the original price \( x \), we need to solve for \( x \):
[tex]\[ x = \frac{1479}{1.16} \][/tex]
5. Performing the division, we get:
[tex]\[ x = 1275.0 \][/tex]
So, the original price of the article was ₹1275.
### Problem 18:
Question: Pratibha reduced her weight by 15%. If now she weighs 59.5 kg, what was her earlier weight?
Solution:
1. Let Pratibha's original weight be \( y \).
2. She reduced her weight by 15%, which means she now weighs 85% of her original weight.
This can be written as:
[tex]\[ 0.85y = 59.5 \][/tex]
3. To find the original weight \( y \), we solve for \( y \):
[tex]\[ y = \frac{59.5}{0.85} \][/tex]
4. Performing the division, we get:
[tex]\[ y = 70.0 \][/tex]
So, Pratibha's original weight was 70.0 kg.
In summary:
- The original price of the article was ₹1275.
- Pratibha's original weight was 70.0 kg.
