Soldiers in concentric circles

XAT 2026 · Quantitative Ability & Data Interpretation · Easy · Geometry

In a battle, the commander-in-chief arranges his soldiers in a formation of three concentric circles. The radii of the circles are in an arithmetic progression: the smallest radius is 70 m70\text{ m} (meters) and the largest is 140 m140\text{ m}. If each soldier is to be separated from the adjacent soldiers standing on the same circle by 1 m1\text{ m}, how many soldiers are required to complete the formation? (Consider π=22/7\pi = 22/7.)

  1. A.

    660

  2. B.

    1320

  3. C.

    880

  4. D.

    1980

  5. E.

    440

Answer

D

Explanation

Let the three concentric circles be C1,C2,C3C_1, C_2, C_3 with radii r1,r2,r3r_1, r_2, r_3. Given r1=70 mr_1 = 70\text{ m} and r3=140 mr_3 = 140\text{ m}, and since r1,r2,r3r_1, r_2, r_3 are in AP, r2=70+1402=105 mr_2 = \frac{70 + 140}{2} = 105\text{ m}.

The total perimeter of all three circles is: Total Circumference=2π(r1+r2+r3)=2×227×(70+105+140)=2×227×315=1980 m\text{Total Circumference} = 2\pi(r_1 + r_2 + r_3) = 2 \times \frac{22}{7} \times (70 + 105 + 140) = 2 \times \frac{22}{7} \times 315 = 1980\text{ m}

Since soldiers are separated by 1 m1\text{ m} on each circumference, the number of soldiers required is 19801980.

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