A,B and C shared the profit in a business in the ratio 5:7:8 and partnered for 14 months, 8 months and 7 months. Ratio of their invesments is:a)19:49:64b)20:49:64c)20:49:65d)20:50:64Correct answer is option 'B'. Can you explain this answer?

Question

Answer

Given:
- Profit sharing ratio: 5:7:8
- Partnership duration: 14 months, 8 months, and 7 months

To Find:
- Ratio of their investments

Solution:
Let's assume the investments made by A, B, and C are x, y, and z respectively.

Step 1:
Since the profit sharing ratio is given, we can write the equation:
5x × 14 : 7y × 8 : 8z × 7 = 5 : 7 : 8

Simplifying the equation, we get:
70x : 56y : 56z = 5 : 7 : 8

Step 2:
To make the equation simpler, we can divide both sides by the common factor 7:
10x : 8y : 8z = 5 : 7 : 8

Step 3:
Since the partnership durations are given, we can write the equation:
10x × 14 : 8y × 8 : 8z × 7 = 14 : 8 : 7

Simplifying the equation, we get:
140x : 64y : 56z = 14 : 8 : 7

Step 4:
To make the equation simpler, we can divide both sides by the common factor 8:
17.5x : 8y : 7z = 14 : 8 : 7

Step 5:
Comparing the equations from step 2 and step 4, we can equate the values:
10x = 17.5x
This implies 10x / 17.5x = 1

Similarly,
8y / 8y = 1
7z / 7z = 1

Step 6:
Simplifying the equation, we get:
10 / 17.5 = 1 / x

Cross-multiplying, we get:
10x = 17.5

Simplifying further, we get:
x = 17.5 / 10
x = 1.75

Step 7:
Substituting the value of x in the equation from step 2, we get:
10(1.75) : 8y : 8z = 5 : 7 : 8

Simplifying the equation, we get:
17.5 : 8y : 8z = 5 : 7 : 8

Step 8:
Since we need to find the ratio of the investments, we can multiply each side by a common factor to get whole numbers. Let's multiply each side by 2:
35 : 16y : 16z = 10 : 14 : 16

Step 9:
Comparing the values, we get:
16y = 14 × 16
16y = 224
y = 224 / 16
y = 14

Similarly,
16z = 16 × 16
16z = 256
z = 256 / 16
z = 16

Step 10:
Now we have the values

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