The weight of Ayush and Abhishek are in the ratio of 8 ∶ 5. Abhishek's weight increases by 40 percent and the total weight of Ayush and Abhishek both increase by 60 percent. If the total weight becomes 104 kg, then what is the weight of Ayush after the increment?

Given:

The weight of Ayush and Abhishek is in the ratio of 8:5.

Abhishek's weight increased by 40%.

The total weight of Ayush and Abhishek both increased by 60%.

The total weight becomes 104 kg.

Formulas:

Increase in weight = Original weight × Percentage increase/100

Solution:

Let's assume:

The weight of Ayush = 8x

The weight of Abhishek = 5x

Abhishek's weight after the increase:

Increase in weight = 5x × 40/100

Increase in weight = 2x

New weight of Abhishek = 5x + 2x = 7x

Total weight of Ayush and Abhishek after the increase:

Increase in weight = (8x + 5x) × 60/100

Increase in weight = 13x × 60/100

Increase in weight = 7.8x

Total weight after the increase:

Total weight = 8x + 5x + 7.8x

Total weight = 20.8x

Given that the total weight becomes 104 kg, we can set up the equation:

20.8x = 104

To solve for x, we divide both sides of the equation by 20.8:

x = 104/20.8

x = 5

Now that we know x, we can find the weight of Abhishek after the increment:

Weight of Abhishek = 7x

Weight of Abhishek = 7 × 5

Weight of Abhishek = 35 kg

The total weight after the increment is 104.

So, the weight of Ayush after the increment is 104 - 35 = 69

Therefore, the weight of Ayush after the increment is 69 kg.