Three friends Alice, Bond and Charlie divide $1105 among them. When $10, $20 and $15 are removed from the sums that Alice, Bond and Charlie received, the share of the sums that they receive is in the ratio of 11 : 18 : 24. What did Charlie receive?

Question

Three friends Alice, Bond and Charlie divide $1105 amongs them. When $10, $20 and $15 are removed from the sums that Alice, Bond and Charlie received respectively, then the share of the sums that they receive is in the ratio of 11 : 18 : 24. How much did Charlie receive?

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Answer 1 · 2016-05-10T22:01:53

$$495$

Note that:

$$1105 - $10 - $20 - $15 = $1060$

Note that:

$11+18+24 = 53$

So:

$($1060)/(11+18+24) = ($1060)/53 = $20$

So after the $$10$ , $$20$ and $$15$ are removed, the amounts Alice, Bond and Charlie receive are:

${ ("Alice: " $20 * 11 = $220), ("Bond: " $20 * 18 = $360), ("Charlie: " $20 * 24 = $480) :}$

Adding the $$10$ , $$20$ and $$15$ back, the original amounts that they received were:

${ ("Alice: " $220 + $10 = $230), ("Bond: " $360+$20 = $380), ("Charlie: " $480 + $15 = $495) :}$