Question

Two houses A and B were constructed at a total cost of Rs 100000 and Rs 250000 respectively The expenditure on materials is shown in the pie charts given bellow
The expenditure on B exceeds expenditure on A by :

• A. Rs $12500$
• B. Rs $15000$
• C. Rs $10000$
• D. Rs $22000$

Answer 1

The correct option is A Rs $12500$

Answer:-

Shaded area = Materials

Given:- Area of circle A = Total cost of construction of A = Rs $100000$

$\pi {r_1}^2=100000$

$\Rightarrow {r_1}^2=\frac{100000}{\pi }$

Now expenditure on material for A = Area covered by material in circle A = $\frac{\pi {r_1}^2}{2}$

$E_A=\frac{\pi \times 100000}{2\times \pi }=50000$

Similarly: Area of B = Total cost of construction of A = Rs $250000$

$\pi {r_2}^2=250000$

${r_2}^2=\frac{250000}{\pi }$

Now expenditure on material for B = Area covered by material in circle B = $\frac{\pi {r_1}^2}{4}$

$E_B=\frac{\pi \times 250000}{4\times \pi }=62500$

Answer: expenditure on material for B - expenditure on material for A = $62500-50000=12500$