I bought a certain number of marbles at rate of 59 marbles for rupees 2 times M, where M is an integer. I divided these marbles into two parts of equal numbers, one part of which I sold at the rate of 29 marbles for Rs. M, and the other at a rate 30 marbles for Rs. M. I spent and received an integral number of rupees but bought the least possible number of marbles. How many did I buy?
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Answer:
102660
Step-by-step explanation:
59X Marbles bought for 2MX Rs
One part = 59X/2
Another Part = 59X/2
Sold for (M/29) (59X/2) & (M/30)(59X/2) respectively
59MX/58 & 59MX/60
LCM of 58 & 60
58 = 2 * 29
60 = 2* 30
LCM = 30*29 * 2 = 1740
=> MX = 1740
59MX/58 = 1770
59MX/60 = 1711
Marbles Sold = 1770 * 29 = 51330
& 1711 * 30 = 51330
Total Marbles = 51330 + 51330 = 102660
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