A,B and

A, B, and C invested capital in the ratio 1/3 : 1/4 : 1/5. After 4 months, A withdraws half of his capital. If the yearly profit is Rs 8,470, find A's share.

Final Answer:

a =  2800 Rs

Step-by-step explanation:

$$\begin{gathered} X=8470\text{Rs} \\ a:b:c=1/3:1/4:1/5 \\ 3...\text{ prime number} \\ 4=2^2 \\ 5...\text{ prime number} \\ LCM(3,4,5)=2^2\cdot 3\cdot 5=60 \\ LCM(3,4,5)=3\cdot 4\cdot 5 \\ a:b:c=20:15:12 \\ a:b:c=20x:15x:12x \\ d=\frac{X}{20\cdot 4+10\cdot 8+15\cdot 12+12\cdot 12}=\frac{8470}{20\cdot 4+10\cdot 8+15\cdot 12+12\cdot 12}=\frac{35}{2}=17.5 \\ a=(20\cdot 4+10\cdot 8)\cdot d=(20\cdot 4+10\cdot 8)\cdot 17.5=2800\text{Rs} \\ b=15\cdot 12\cdot d=15\cdot 12\cdot 17.5=3150\text{Rs} \\ c=12\cdot 12\cdot d=12\cdot 12\cdot 17.5=2520\text{Rs} \end{gathered}$$

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