Management Aptitude Test 2016 Paper

(b) ∵ Length of circle with 4 balloons = 10 cm
⇒ 2πr = 10 ⇒ r = $\frac{5}{\mathit{\pi }}$
∵ Radius of innermost circle = 5 cm
∴ Number of balloons in a circle of radius 5 cm = 4π
Similarly, number of balloons in a circle of radius 16 cm
= $\frac{4}{5}$ × 16π = $\frac{64}{5}$ π
[∵ 12 circles are to be formed]
So, 4π , $\frac{24}{5}$π ........ $\frac{64}{5}$π forms an AP with a = 4π
l = $\frac{64}{5}$π and n = 12
∴ Total number of balloons
= $\frac{\mathit{n}}{2}$ [a + l]
= $\frac{12}{2}\left[4\mathit{\pi }+\frac{64}{5}\mathit{\pi }\right]$
= 6 $\left[\frac{20\mathit{\pi }+64\mathit{\pi }}{5}\right]$
= 6 × $\frac{84}{5}\mathit{\pi }$ ≈ 317