The number of oranges in three basket are in the ratio 3 : 4 : 5. In which ratio the no. of oranges in first two basket must be increased so that the new ratio becomes 5 : 4 : 3 ?2:13:41:32:3
Question
The number of oranges in three basket are in the ratio 3 : 4 : 5. In which ratio the no. of oranges in first two basket must be increased so that the new ratio becomes 5 : 4 : 3 ?2:13:41:32:3
Solution
Let's denote the number of oranges in the first, second, and third baskets as 3x, 4x, and 5x respectively.
The new ratio is 5:4:3, so let's denote the new number of oranges in the first, second, and third baskets as 5y, 4y, and 3y respectively.
We know that the number of oranges in the third basket decreases, so 5x must be greater than 3y.
However, we are interested in the increase in the first two baskets, so we need to find the values of y and x that satisfy the following two equations:
3x + a = 5y (for the first basket) 4x + b = 4y (for the second basket)
where a and b are the number of oranges added to the first and second baskets respectively.
From the second equation, we can express y in terms of x and b:
y = (4x + b) / 4
Substituting this into the first equation gives:
3x + a = 5 * ((4x + b) / 4)
Solving this equation will give us the values of a and b, which represent the number of oranges that need to be added to the first and second baskets respectively to achieve the new ratio.
The ratio in which the number of oranges in the first two baskets must be increased is then given by a : b.
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