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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?

Solution

✅ Correct Option: 1

Let Bimla take xx days to complete the work alone.

Aditi takes 60% more time than Bimla:

Aditi takes =x+0.6x=1.6x= x + 0.6x = 1.6x days


If someone completes work in xx days, their work rate per day =1x= \dfrac{1}{x}

Bimla's work rate =1x= \dfrac{1}{x}

Aditi's work rate =11.6x= \dfrac{1}{1.6x}


When working together, the combined work rate equals the sum of individual rates.

They complete the work together in 16 days, so combined work rate =116= \dfrac{1}{16}

1x+11.6x=116\dfrac{1}{x} + \dfrac{1}{1.6x} = \dfrac{1}{16}


Simplifying the left side:

1x(1+11.6)=116\dfrac{1}{x}\left(1 + \dfrac{1}{1.6}\right) = \dfrac{1}{16}

Since 1.6=851.6 = \dfrac{8}{5}, we have 11.6=58\dfrac{1}{1.6} = \dfrac{5}{8}

1x(1+58)=116\dfrac{1}{x}\left(1 + \dfrac{5}{8}\right) = \dfrac{1}{16}

1x(138)=116\dfrac{1}{x}\left(\dfrac{13}{8}\right) = \dfrac{1}{16}

138x=116\dfrac{13}{8x} = \dfrac{1}{16}


Cross multiplying:

13×16=8x13 \times 16 = 8x

208=8x208 = 8x

x=26x = 26

Therefore, Bimla takes 26 days to complete the work alone.

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