A, B and C shared the profit in a business in the ratio 5 : 7 : 8. They had partnered for 14 months, 8 months and 7 months respectively. What was the ratio of their investments? Choose the correct choice from the following
A) 20:64:49
B) 49:20:64
C) 64:20:49
D) 64:49:20
E) 20:49:64
Ratio in which A,B and C shared the profit =5:7:8   Assume that the ratio of their investments =a:b:c   ⇒14a:8b:7c=5:7:8⋯(A)   From (A),   14a:8b=5:7   ⇒14a×7=8b×5   ⇒7a×7=4b×5   ⇒b=49a/20⋯(1)   From (A),   14a:7c=5:8   ⇒(14a)×8=(7c)×5   ⇒(2a)×8=c×5   ⇒c=16a/5⋯(2)   a:b:c=a:49a/20:16a/5   =1:49/20:16/5   =20:49:64   Answer is 20:49:64.
<result>E</result>
A, B and C shared the profit in a business in the ratio 5 : 7 : 8. They had partnered for 14 months, 8 months and 7 months respectively. What was the ratio of their investments?