Savvy invested $\frac{1}{3}rd$ of her capital at 10% gain, $\frac{1}{4}th$ at 20% gain and the remaining at 30% gain. If her income from gain is ₹50,000, then value of capital is :

₹2,40,000

Let the capital be P

P/3 * 10% + P/4 * 20% + (P - P/3 - P/4)*30% = 50000

P/30 + P/20 + (12P-4P-3P)*0.3/12 = 50000

P/30 + P/20 + (5P)*0.3/12 = 50000

P/30 + P/20 + 15P/120 = 50000

(4P+6P+15P)/120 = 50000

25P = 6000000

P = 240000

The correct answer is option (2) : ₹2,40,000