A borrows RS8000 at 12% per annum simple intrest and B borrows RS 9100 at 10% per annum simple intrest.In how many years will their amount be equal

*A*and

*B*be equal after

*t*years.

Now simple interest for

*A*after

*t*years = $\frac{8000\times 12\times t}{100}=960t$

Then, the total amount of

*A*= 8000 + 960

*t*......(i)

Similarly the simple interest for B after

*t*years = $\frac{9100\times 10\times t}{100}=910t$

Then, the total amount of

*B*= 9100 + 910

*t*.....(ii)

Now, equating (i) and (ii) we have;

$8000+960t=9100+910t\phantom{\rule{0ex}{0ex}}\Rightarrow 960t-910t=9100-8000\phantom{\rule{0ex}{0ex}}\Rightarrow 50t=1100\phantom{\rule{0ex}{0ex}}\Rightarrow t=\frac{1100}{50}=22$

So the amount of

*A*and

*B*will be equal after 22 years.

**
**