Three friends P, Q and R divide \$1105 amongst them in such a way that if \$10, $20 and $15 are removed from the sums that P, Q and R received respectively, then the share of the sums that they got will be in the ratio of 11 : 18 : 24. How much did R receive?

Let the initial amounts received by P, Q and R be such that after removing $10, $20 and \$15, their remaining sums are 11k, 18k and 24k. The sum of these remaining amounts is 11k + 18k + 24k = 53k. The total remaining amount is 1105 - (10 + 20 + 15) = 1060, so 53k = 1060 and k = 20. R's reduced sum is 24 * 20 = 480, meaning R's initial receipt was 480 + 15 = \$495.

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