Question:
X, Y, and Z form a partnership. X invests Rs. 72,000, Y invests Rs. 54,000, and Z invests Rs. 36,000. After 4 months, Y increases his investment by 20%, while Z reduces his investment by 15%. At the end of 1 year, the total profit earned is Rs. 1,08,000. What is Z’s share of the profit?
X, Y और Z एक साझेदारी बनाते हैं। X रु. 72,000, Y रु. 54,000 और Z रु. 36,000 का निवेश करता है। 4 महीने बाद, Y अपने निवेश में 20% की वृद्धि करता है, जबकि Z अपने निवेश में 15% की कमी करता है। 1 वर्ष के अंत में, कुल अर्जित लाभ रु. 1,08,000 है। लाभ में Z का हिस्सा क्या है?
Options:
- \(\text{Rs. }\dfrac{4,84,000}{23}\)
- \(\text{Rs. }\dfrac{4,86,000}{23}\)
- \(\text{Rs. }\dfrac{4,87,000}{23}\)
- \(\text{Rs. }\dfrac{4,85,000}{23}\)
- \(\text{Rs. }\dfrac{4,84,000}{23}\)
- \(\text{Rs. }\dfrac{4,86,000}{23}\)
- \(\text{Rs. }\dfrac{4,87,000}{23}\)
- \(\text{Rs. }\dfrac{4,85,000}{23}\)
Correct Answer: b)
Explanation:
Dividing all investments by 1000 for convenience:
X’s ratio unit \(= 72 \times 12 = 864\).
Y’s ratio unit \(= (54 \times 4) + (54 \times 1.20 \times 8) = 216 + (64.8 \times 8) = 216 + 518.4 = 734.4\).
Z’s ratio unit \(= (36 \times 4) + (36 \times 0.85 \times 8) = 144 + (30.6 \times 8) = 144 + 244.8 = 388.8\).
Total units \(= 864 + 734.4 + 388.8 = 1987.2\).
Z’s share \(= 108000 \times \dfrac{388.8}{1987.2} = 108000 \times \dfrac{3888}{19872}\).
Dividing numerator and denominator by 864: \(19872 / 864 = 23\) and \(3888 / 864 = 4.5\).
Z’s share \(= 108000 \times \dfrac{4.5}{23} = \dfrac{4,86,000}{23}\).
महीनों के आधार पर निवेश:
X \(= 72 \times 12 = 864\)
Y \(= (54 \times 4) + (64.8 \times 8) = 216 + 518.4 = 734.4\)
Z \(= (36 \times 4) + (30.6 \times 8) = 144 + 244.8 = 388.8\)
कुल अनुपात \(= 864 + 734.4 + 388.8 = 1987.2\)
Z का हिस्सा \(= 108000 \times \dfrac{388.8}{1987.2} = \text{Rs. }\dfrac{4,86,000}{23}\)।