Question

A house costs 36% more today than when it was built. If the cost of the house today is $333 200, find the cost when it was built.

Answer 1

$\\ \\ \large\underline{ \underline{ \sf{ \red{given:} }}}$

• House costs 36% more today when it was built.

• Cost of house is 333200$.

$\\ \\ \large\underline{ \underline{ \sf{ \red{to \: find:} }}}$

• Cost of house when it was built.

$\\ \\ \large\underline{ \underline{ \sf{ \red{solution:} }}}$

Let cost of house when it was built be 'x'.

The cost of house in present(333200$) is 36% more than 'x'

Hence , x + 36% of x = 333200$

$\\ \\ \sf \: x + \frac{36}{100} (x) = 333200 \\ \\ \\ \sf \: \frac{100x + 36x}{100} = 333200 \\ \\ \\ \sf \: \frac{136x}{100} = 333200 \\ \\ \\ \sf \: 136 x= 33320000 \\ \\ \\ \sf \: x = \frac{33320000}{136} \\ \\ \\ \sf \: \underline\orange{x = 245000 }$

Hence , cost of house when it was built is 245000$.

$\\ \\ \large\underline{ \underline{ \sf{ \red{verification:} }}}$

Cost of built + 36% of cost of built = Present cost

245000 + 36% of 245000 = 333200

$\\ \\ \sf \: 245000 + \frac{36}{100} (245000) = 333200 \\ \\ \\ \sf \: 245000 + 36(2450) = 333200 \\ \\ \\ \sf \: 245000 + 88200 = 333200 \\ \\ \\ \sf \: 333200 = 333200 \: \: \: \: \: \: \: \: \: \: \: \: (verified)$