Alok lent out a certain sum. He lent 1/3 of his sum at 7% simple interest, 1/4 at 8% simple interest and the remaining at 10% simple interest. If ₹510 is his total annual interest, then the total money lent out is:

Let the total money lent out be = x Amount lent at 7%: = (1/3)x Interest = (1/3)x × 7/100 = 7x/300 Amount lent at 8%: = (1/4)x Interest = (1/4)x × 8/100 = 8x/400 = x/50 Remaining amount: Fraction remaining = 1 − 1/3 − 1/4 = 1 − 7/12 = 5/12 Amount = (5/12)x Interest at 10% = (5/12)x × 10/100 = 50x/1200 = x/24 Total interest = 510: 7x/300 + x/50 + x/24 = 510 LCM of 300, 50 and 24 is 600: 7x/300 = 14x/600 x/50 = 12x/600 x/24 = 25x/600 So, (14x + 12x + 25x) / 600 = 510 51x / 600 = 510 x = 510 × 600 / 51 x = 10 × 600 x = 6000 Total money lent out = ₹6000