Question

A radioactive sample disintegrates by $10$% during one month. How much fraction will disintegrate in four months.

• A. $34.39$%
• B. $40$%
• C. $38$%
• D. $50$%

Answer 1

The correct option is A $34.39$%

Please note that 10% means 0.1 part.

If 0.1part is lost, then 0.9 will remain.

Also note that 10% of 0.9 is 0.09.

If that is lost from 0.9 part, then 0.81 will remain

$x-0.1x=0.9x$

$0.9x-0.09x=0.81x$

$0.81x-0.081x=0.729x$

$0.729x-0.0729x=0.6561x$

Thus after 4 months 0.6561 part will remain.

This means, 0.3439 will be lost.

This means 34.39% is lost after 4 months