Three friends X, Y and Z started a business by investing a sum of money in the ratio of 4: 2 : 5.
Three friends X, Y and Z started a business by investing a sum of money in the ratio of 4: 2 : 5. After 6 months, X withdraws half of his capital. If the sum invested by Z is ₹23,000, then out of a total annual profit of ₹37,000, what is the difference between X’s and Y’s profit?
तीन मित्र X, Y और Z ने 4 : 2 : 5 के अनुपात में धन निवेश करके एक व्यवसाय शुरू किया। 6 महीने बाद, X अपनी पूंजी का आधा भाग निकाल लेता है। यदि Z द्वारा निवेश की गई राशि ₹23,000 है, तो कुल वार्षिक लाभ ₹37,000 में से X और Y के लाभ के बीच कितना अंतर होगा?
Detailed Solution & Logic
Correct Answer:
₹3700
दिया गया अनुपात:
X : Y : Z = 4 : 2 : 5
Z का निवेश = ₹23,000
तो 5 भाग = ₹23,000
1 भाग = ₹23,000 ÷ 5 = ₹4,600
अब,
X = 4 × 4600 = ₹18,400
Y = 2 × 4600 = ₹9,200
Z = ₹23,000
अब लाभ बाँटने के लिए निवेश × समय का नियम लगेगा।
X का निवेश
पहले 6 महीने: ₹18,400
अगले 6 महीने X ने आधी पूंजी निकाल ली:
शेष = ₹18,400 ÷ 2 = ₹9,200
तो X का निवेश-समय:
= (18,400 × 6) + (9,200 × 6)
= 18,400(6+3)
= 18,400 × 9
= 165,600
Y का निवेश-समय
= 9,200 × 12
= 110,400
Z का निवेश-समय
= 23,000 ×12
= 276,000
अब अनुपात:
165600 : 110400 : 276000
सभी को 55,200 से भाग देने पर:
= 3 : 2 : 5
कुल लाभ = ₹37,000
कुल भाग = 3+2+5 = 10
एक भाग = ₹37,000 ÷10
= ₹3,700
X का लाभ = 3×3700 = ₹11,100
Y का लाभ = 2×3700 = ₹7,400
अंतर = ₹11,100 − ₹7,400
= ₹3,700
सही उत्तर: ₹3700
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