If A, B, and C are positive integers and 7A=4B=8C, then the least possible value of A+B+C=?

M4maths Previous Puzzles

06 Jul 2022 Ratio & Proportion

If A, B, and C are positive integers and 7A=4B=8C, then the least possible value of A+B+C=?

OPtion

1) 58
2) 19
3) 38
4) 56
5) 28
6) 57
7) 29
8) 87
9) 17
10) None of these

Solution

Let 7A=4B=8C=k then A=k/7, B=k/4, C=k/8.
A : B : C = k/7 : k/4 : k/8
Multiply the ratio by 56 (LCM of 7,4,8)
A : B : C = 8k : 14k : 7k
The minimum possible values of A, B & C are for k=1
.'. A=8, B=14, C=7 and minimum sum=8+14+7=29

Correct Option: 7 Best Solution (1)