A and B started a business by investing ₹48,000 and ₹72,000 respectively. After 6 months, A withdrew half of his capital, while B…

Question

A and B started a business by investing ₹48,000 and ₹72,000 respectively. After 6 months, A withdrew half of his capital, while B increased his capital by ₹24,000. At the end of the year, they earned a total profit of ₹55,000. What is B's share in the profit?

1. A. ₹26,500
2. B. ₹28,000
3. C. ₹38,500 (Correct answer)
4. D. ₹36,000

Correct Answer

Option C — ₹38,500

Detailed Solution & Explanation

The correct answer is ₹38,500.

Key Points

• Capital changes mid-year, so compute each partner's capital × time in two halves:
  • A: 48,000 × 6 + 24,000 × 6 = 288,000 + 144,000 = 432,000
  • B: 72,000 × 6 + 96,000 × 6 = 432,000 + 576,000 = 1,008,000
• Ratio A : B = 432 : 1,008 = 3 : 7, totalling 10 parts.
• B's share = 7/10 × 55,000 = ₹38,500.

Additional Information

• "Withdrew half his capital" leaves 24,000, and "increased by ₹24,000" makes B's second-half capital 96,000 — read both phrasings carefully, as one is a proportion and the other an absolute amount.
• The general rule for any number of capital changes is to break the year into intervals of constant capital, compute capital × months for each, and sum.
• A quick sanity check: B invested more and then added further, so B's share must exceed half the profit — which immediately rules out ₹26,500.

प्रश्न (हिन्दी में)

A और B ने क्रमशः ₹48,000 और ₹72,000 का निवेश करके एक व्यवसाय शुरू किया। 6 महीने बाद, A ने अपनी आधी पूंजी निकाल ली, जबकि B ने अपनी पूंजी में ₹24,000 की वृद्धि की। वर्ष के अंत में, उन्होंने कुल ₹55,000 का लाभ कमाया। लाभ में B का हिस्सा क्या है?

1. A. ₹26,500
2. B. ₹28,000
3. C. ₹38,500
4. D. ₹36,000