Three friends Ram, Rahul and Raj divide $1000 amongs them in such a way that if $1, $2 and $8 are removed from the sums that Ram, Rahul and Raj received respectively, then the share of the sums that they got will be in the ratio of 6 : 7 : 10. How much did Raj receive? Choose the correct choice:  A) $434  B) $458  C) $438  D) $448  E) $478
Explanatory Answer   Let the sums of money received by A, B and C be x, y and z respectively.   Then x - 1 : y - 2 : z -8 is 6a : 7a : 10a   When $1, $2 and $8 are removed, we are removing a total of $11 from $1000.   Therefore, 6a + 7a + 10a = 1000 - 11= 
<gadget id="calculator">1000 - 11</gadget>
<output>989</output>
989   i.e., 23a= 989   or a = 43   We know that z - 8 = 10a = 10 * 43= 
<gadget id="calculator">10 * 43</gadget>
<output>430</output>
430   Therefore, z= 430 + 8= 
<gadget id="calculator">430 + 8</gadget>
<output>438</output>
$438   The correct choice is (c)
<result>C</result>
Three friends Ram, Rahul and Raj divide $1000 amongs them in such a way that if $1, $2 and $8 are removed from the sums that Ram, Rahul and Raj received respectively, then the share of the sums that they got will be in the ratio of 6 : 7 : 10. How much did Raj receive?