Question

If $1³+2³+.......+9³=2025$, then $(0.11)³+(0.22)³+......+(0.99)³$will be-

• A. $0.2695$
• B. $2.695$
• C. $3.695$
• D. $0.3695$

Answer 1

The correct option is B

$2.695$

Given that $1³+2³+.......+9³=2025$………(1)

We have to find $(0.11)³+(0.22)³+......+(0.99)³$…….(2)

We will simplify (2) and get

$=(0.11)³+(0.22)³+......+(0.99)³$

$$\begin{gathered} ={\left(\frac{11}{100}\right)}^3+{\left(\frac{22}{100}\right)}^3+.......+{\left(\frac{99}{100}\right)}^3 \\ ={\left(\frac{11}{100}\right)}^3\left(1^3+2^3+.......9^3\right) \end{gathered}$$

$={\left(\frac{11}{100}\right)}^3\times 2025$ [Putting the value according to equation (1)]

$$\begin{gathered} =\frac{1331}{1000000}\times 2025 \\ =2.695 \end{gathered}$$

Hence, B is the correct option