CUET UG 2025 — General Test Arithmetic

Let Bimla take $x$x 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

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If someone completes work in $x$x days, their work rate per day $= \dfrac{1}{x}$=x1​

Bimla's work rate $= \dfrac{1}{x}$=x1​

Aditi's work rate $= \dfrac{1}{1.6x}$=1.6x1​

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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 $= \dfrac{1}{16}$=161​

$$\dfrac{1}{x} + \dfrac{1}{1.6x} = \dfrac{1}{16}$$x1​+1.6x1​=161​

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Simplifying the left side:

$$\dfrac{1}{x}\left(1 + \dfrac{1}{1.6}\right) = \dfrac{1}{16}$$x1​(1+1.61​)=161​

Since $1.6 = \dfrac{8}{5}$1.6=58​, we have $\dfrac{1}{1.6} = \dfrac{5}{8}$1.61​=85​

$$\dfrac{1}{x}\left(1 + \dfrac{5}{8}\right) = \dfrac{1}{16}$$x1​(1+85​)=161​

$$\dfrac{1}{x}\left(\dfrac{13}{8}\right) = \dfrac{1}{16}$$x1​(813​)=161​

$$\dfrac{13}{8x} = \dfrac{1}{16}$$8x13​=161​

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Cross multiplying:

$$13 \times 16 = 8x$$13×16=8x

$$208 = 8x$$208=8x

$$x = 26$$x=26

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