Question

A building worth Rs 133100 is constructed on land worth Rs 72900. After how many years will the value of both be same if the land appreciates at 10% p.a and building depreciates at 10% p.a.?

• A. $1\frac{1}{2}$ years
• B. 2 years
• C. $2\frac{1}{2}$ years
• D. $2.92yrs\simeq 3yrs$

Answer 1

Answer: (D)

$2.92yrs\simeq 3yrs$

We take the required number of years=x.

We know that $Finalvalue=initialvalue\pm \left(\right(initialvalue)\times \frac{time\times rate}{100}).$

The value of the building depriciates.

$\therefore$ The rate will be negative.

So, for the building, the value after x yrs. will be

=$133100-133100\times \frac{10}{100}\times x=133100-13310x.......\left(i\right)$

For the land the value increases

$\therefore$ The rate is positive.

So, for the land, the value after x yrs. will be

$72900+72900\times \frac{10}{100}\times x=72900+7290x.......\left(i\right).$

$\therefore$ By the given condition,

$133100-13310x=72900+7290x$

$⟹20600x=60200⟹x=\frac{60200}{20600}yrs.=2.92yrs\simeq 3yrs$

Ans- Option D.