To complete a work, Aditi takes 60% more time than Bimla. If both of them work together, they take 16 days to complete the work. How much time shall Bimla take to do it alone?
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → 26 days
Let Bimla’s time = x days
Aditi takes 60% more time, so
$\text{Aditi’s time} = 1.6x$
Work rates
$\text{Bimla’s rate} = \frac{1}{x}$
$\text{Aditi’s rate} = \frac{1}{1.6x} = \frac{5}{8x}$
Combined work rate
$\frac{1}{x} + \frac{5}{8x} = \frac{8+5}{8x} = \frac{13}{8x}$
Given, together they finish work in 16 days:
$\frac{13}{8x} = \frac{1}{16}$
Solve for x
$13 \times 16 = 8x$
$208 = 8x$
$x = 26$
Correct answer: 26 days