Multiple choice

P invests Rs. 24000 in a business. After 6 months Q joins the business with Rs. 8000, but Q increases his investment by Rs. 2000 after every 2 months. Find the profit share of Q after 20 months if the total profit is Rs. 67600.

  1. Rs. 19600

  2. Rs. 48000

  3. Rs. 25800

  4. Rs. 32600

  5. None of these
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

P invests Rs. 24000 for 20 months, so equivalent capital = 24000 × 20 = 480000. Q joins after 6 months, so invests for 14 months total. Q's investment: Rs. 8000 for first 2 months, Rs. 10000 for next 2 months, Rs. 12000 for next 2 months, Rs. 14000 for next 2 months, Rs. 16000 for final 6 months (months 12-18, but wait - Q joins at month 6, invests till month 20 = 14 months). Let's recalculate: months 7-8: 8000, 9-10: 10000, 11-12: 12000, 13-14: 14000, 15-20: 16000. Equivalent = 8000×2 + 10000×2 + 12000×2 + 14000×2 + 16000×6 = 16000 + 20000 + 24000 + 28000 + 96000 = 184000. Ratio P:Q = 480000:184000 = 120:46 = 60:23. Q's share = 67600 × 23/83 ≈ 18740 (not matching). Let me reconsider: Q invests 8000 at month 6, increases by 2000 every 2 months. At month 20 (14 months later), Q has had: 8000×2 + 10000×2 + 12000×2 + 14000×2 + 16000×2 + 18000×2 + 20000×2 = 16+20+24+28+32+36+40 = 196. Q's equivalent = 196000. P's = 24000×20 = 480000. Ratio = 480000:196000 = 120:49. Q's share = 67600 × 49/169 = 19600. This matches option A.

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