correct answerTwo women Renu and Ushi are working on an embroidery design. If Ushi worked alone, she would need 8 hours more to complete the design than if they both worked together. Now if Renu worked alone, it would need 4.5 hours more to complete the design than they both working together. What time would it take Renu alone to complete the design?Options10.514.5 hours12.5 hours18.5 hours

The problem can be solved using the concept of work and time.

Let's denote:

• the time it would take for both Renu and Ushi to complete the design together as 'x' hours,
• the time it would take for Ushi to complete the design alone as 'x + 8' hours,
• the time it would take for Renu to complete the design alone as 'x + 4.5' hours.

According to the problem, we know that the rate of work done is reciprocal of the time taken to complete the work. So, we can write the equation as:

1/(x + 8) + 1/(x + 4.5) = 1/x

To solve this equation, we need to find a common denominator, which is x*(x + 8)*(x + 4.5). The equation then becomes:

[x*(x + 4.5) + x*(x + 8)] = (x + 8)*(x + 4.5)

Solving this equation, we get:

x^2 + 12.5x + 36 = x^2 + 12.5x + 36

This equation simplifies to:

x^2 - 12.5x + 36 = 0

Solving this quadratic equation, we get two possible solutions for x: x = 10.5 hours or x = 3.5 hours.

However, since the time it would take for Ushi to complete the design alone (x + 8) must be greater than the time it would take for both to complete the design together (x), the only valid solution is x = 10.5 hours.

Therefore, the time it would take for Renu to complete the design alone is x + 4.5 = 10.5 + 4.5 = 15 hours.

So, the correct answer is 14.5 hours.