In a business A invests ₹ 600 more than B. The capital of B remained invested for $7 \frac{1}{2}$ months, while the capital of A remained invested for 2 more months. If the total profit be ₹ 620 and B gets ₹ 140 less than what A gets, then A's capital is
(a)₹ 2400
(b)₹ 2800
(c)₹ 3000
(d)₹ 3200
Answer
Answer (as printed): C
Explanation
Let B's capital be ₹ $x$. Then, A's capital $=₹(x+600)$. $\therefore \mathrm{A}: \mathrm{B}=\left[(x+600) \times \frac{19}{2}\right]:\left(x \times \frac{15}{2}\right)=(19 x+11400): 15 x$. $\Rightarrow 62(4 x+11400)=14(34 x+11400) \Rightarrow 248 x+706800=476 x+159600 \Rightarrow 228 x=547200 \Rightarrow x=2400$. Hence, A's capital $=₹(2400+600)=₹ 3000$.
Explanation as extracted from the printed page; notation may be imperfect.