Divide one hundred loaves of bread among five persons so that the second person receives as much more than the first as the third receives more than the second and the fourth more than the third and the fifth more than the fourth. Also, the ratio of loaves received by the first two to those received by the last three is 4 : 21. How much does the fourth person get?

• from the ques. it is clear that loaves of bread are in A.P .
  so, 5 terms in A.P is (a-2d), (a-d),(a),(a+d),(a+2d).
  given, sum of these A.P is 100.
  so, a=20
  now, sum of first two terms is (a-2d)+(a-d)=2a-3d
  and sum of last three terms is (a)+(a+d)+(a+2d)=3a+3d
  and their ratio is given: 4:21
  so, (2a-3d)/(3a+3d)=4/21
  putting value of a, we get d=8.
  find fourth person value: a+d=20+8=28 ans................
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