A school has ₹ 1,600 to give 8 cash prizes to students. Each prize is ₹ 30 less than the prize before it. Find the value of each prize.

Doubtly Asked 29 Oct 2026 Practice test ssc 10th Save WhatsApp Report

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Answer: ₹ 305, 275, 245, 215, 185, 155, 125, 95

The prizes form an A.P. with \(n = 8\), \(d = -30\), \(S_8 = 1600\).

\(1600 = \dfrac{8}{2}[2a + 7(-30)] = 4(2a - 210)\)

\(400 = 2a - 210 \Rightarrow 2a = 610 \Rightarrow a = 305\)

Prizes: 305, 275, 245, 215, 185, 155, 125, 95 (last prize \(t_8 = 305 - 210 = 95\)).

Check: \(\dfrac{8}{2}(305 + 95) = 4 \times 400 = 1600\) ✓.

Doubtly AI · 29 Oct 2026 AI-verified · Nov 2026 Report

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