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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 ?
- a)3 : 4
- b)2 : 3
- c)1 : 3
- d)2 : 1
Correct answer is option 'D'. Can you explain this answer?
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Most Upvoted Answer
The number of oranges in three basket are in the ratio 3 : 4 : 5. In w...
Let, B1 : B2 : B3 = 3x : 4x : 5x and
B1 : B2 : B3 = 5y : 4y : 3y
Number of oranges remain constant in third basket as increase in oranges takes place only in first two baskets.
Hence, 5x = 3y
x = 3y/5 and,
∴ 3x : 4x : 5x (putting the vale of x)
= 9y : 12y : 15y
And,
5y : 4y : 3y (multiple by 5) → 25y : 20y : 15y
∴Increment in first basket = 16
And, Increment in second basket = 8
Thus, Required ratio = 16/8 = 2 : 1
B1 : B2 : B3 = 5y : 4y : 3y
Number of oranges remain constant in third basket as increase in oranges takes place only in first two baskets.
Hence, 5x = 3y
x = 3y/5 and,
∴ 3x : 4x : 5x (putting the vale of x)
= 9y : 12y : 15y
And,
5y : 4y : 3y (multiple by 5) → 25y : 20y : 15y
∴Increment in first basket = 16
And, Increment in second basket = 8
Thus, Required ratio = 16/8 = 2 : 1
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The number of oranges in three basket are in the ratio 3 : 4 : 5. In w...
Given:
The ratio of the number of oranges in three baskets is 3 : 4 : 5.
To find:
In which ratio should the number of oranges in the first two baskets be increased so that the new ratio becomes 5 : 4 : 3?
Solution:
Let's assume the number of oranges in the three baskets as 3x, 4x, and 5x respectively.
Step 1:
Write the given ratio in terms of x:
The original ratio of the number of oranges in the three baskets is 3x : 4x : 5x.
Step 2:
In order to change the ratio to 5 : 4 : 3, we need to increase the number of oranges in the first two baskets. Let's assume the increase in the number of oranges in the first basket by a factor of a and in the second basket by a factor of b.
So, the new number of oranges in the first basket will be (3x + a) and in the second basket will be (4x + b).
Step 3:
The new ratio of the number of oranges in the three baskets is (3x + a) : (4x + b) : 5x.
According to the given condition, the new ratio is 5 : 4 : 3.
So, equating the corresponding terms, we get:
(3x + a) : (4x + b) : 5x = 5 : 4 : 3
Step 4:
Cross-multiplying the ratios, we get:
3(4x + b) = 5(5x)
12x + 3b = 25x
3b = 25x - 12x
3b = 13x
Step 5:
To make the calculation easier, let's assume x = 1.
So, we have:
3b = 13
Step 6:
To find the ratio of the increase in the number of oranges in the first two baskets, divide both sides of the equation by 3:
b = 13/3
So, the ratio of the increase in the number of oranges in the first two baskets is 13/3 : 1.
Therefore, the correct answer is option D) 2 : 1.
The ratio of the number of oranges in three baskets is 3 : 4 : 5.
To find:
In which ratio should the number of oranges in the first two baskets be increased so that the new ratio becomes 5 : 4 : 3?
Solution:
Let's assume the number of oranges in the three baskets as 3x, 4x, and 5x respectively.
Step 1:
Write the given ratio in terms of x:
The original ratio of the number of oranges in the three baskets is 3x : 4x : 5x.
Step 2:
In order to change the ratio to 5 : 4 : 3, we need to increase the number of oranges in the first two baskets. Let's assume the increase in the number of oranges in the first basket by a factor of a and in the second basket by a factor of b.
So, the new number of oranges in the first basket will be (3x + a) and in the second basket will be (4x + b).
Step 3:
The new ratio of the number of oranges in the three baskets is (3x + a) : (4x + b) : 5x.
According to the given condition, the new ratio is 5 : 4 : 3.
So, equating the corresponding terms, we get:
(3x + a) : (4x + b) : 5x = 5 : 4 : 3
Step 4:
Cross-multiplying the ratios, we get:
3(4x + b) = 5(5x)
12x + 3b = 25x
3b = 25x - 12x
3b = 13x
Step 5:
To make the calculation easier, let's assume x = 1.
So, we have:
3b = 13
Step 6:
To find the ratio of the increase in the number of oranges in the first two baskets, divide both sides of the equation by 3:
b = 13/3
So, the ratio of the increase in the number of oranges in the first two baskets is 13/3 : 1.
Therefore, the correct answer is option D) 2 : 1.
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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 ?a)3 : 4b)2 : 3c)1 : 3d)2 : 1Correct answer is option 'D'. Can you explain this answer?
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