The ration of prices of two horses was 16:23.Two years later when the price of the first has risen by 10% and that of the second by rs.477, the ratio of their prices becomes 11:20. Find the original prices of the two horses.
Let their respective prices be 16x and 23x
new price of first horse = 1.1(16x) = 17.6x
new price of second horse = 23x + 477
17.6x/(23x+477) = 11/20
352x = 253x + 5247
99x = 5247
x = 53
the first horse cost 16(53) or 848
the 2nd horse cost 23(53) or 1219
check:
848 : 1219 = 16 : 23
I will leave the check of the 2nd condition up to you.
Its right....thank u sir
Let's denote the original price of the first horse as 16x and the original price of the second horse as 23x, where x is a constant.
According to the given information, after two years:
- The price of the first horse increases by 10%, so its new price is 16x + 0.10(16x) = 16x + 1.6x = 17.6x
- The price of the second horse increases by Rs. 477, so its new price is 23x + 477
The new ratio of their prices is given as 11:20. Therefore, we can set up the equation:
(17.6x) / (23x + 477) = 11/20
To solve this equation, we can cross-multiply:
20 * (17.6x) = 11 * (23x + 477)
352x = 253x + 5247
352x - 253x = 5247
99x = 5247
x = 5247 / 99
x ≈ 53
Now, we can find the original prices of the horses:
- The original price of the first horse = 16x = 16 * 53 = 848 units
- The original price of the second horse = 23x = 23 * 53 = 1219 units
Therefore, the original prices of the two horses were 848 units and 1219 units, respectively.
To solve this problem, we can break it down into two parts:
1. Find the ratio of the original prices of the horses.
2. Use the given information to find the original prices of the horses.
Let's start with the first part:
1. Finding the ratio of the original prices of the horses:
- The given ratio of prices is 16:23.
- Let's assume that the original prices of the two horses are 16x and 23x, respectively.
- This means that the first horse's original price is 16x and the second horse's original price is 23x.
Now, let's move on to the second part:
2. Using the given information to find the original prices of the horses:
- After two years, the price of the first horse has increased by 10%, so its new price is 16x + (0.10)(16x) = 16x + 1.6x = 17.6x.
- The price of the second horse has increased by Rs. 477, so its new price is 23x + 477.
- According to the problem, the new ratio of prices is 11:20.
- Therefore, we have the equation (17.6x)/(23x + 477) = 11/20.
- Cross-multiply and solve the equation to find the value of x.
Once you find the value of x, you can substitute it back into the expressions for the original prices of the horses (16x and 23x) to find their actual values.