For three non-zero real numbers a,b,c, if
2
a
=
3
b
=
4
c
=
k
2a−3b+5c
, then the value of k is
- A10
- B15
- C20
- D25
Solution & Step-by-step Explanation
Let the given equal ratios be equal to a constant proportionality parameter m:
2
a
=
3
b
=
4
c
=m
This allows us to express a,b, and c in terms of m:
a=2m
b=3m
c=4m
Now, substitute these expressions into the final ratio term from the problem:
k
2a−3b+5c
=m
k
2(2m)−3(3m)+5(4m)
=m
k
4m−9m+20m
=m
k
15m
=m
Since m is a non-zero value, we can divide both sides by m:
k
15
=1⟹k=15
2
a
=
3
b
=
4
c
=m
This allows us to express a,b, and c in terms of m:
a=2m
b=3m
c=4m
Now, substitute these expressions into the final ratio term from the problem:
k
2a−3b+5c
=m
k
2(2m)−3(3m)+5(4m)
=m
k
4m−9m+20m
=m
k
15m
=m
Since m is a non-zero value, we can divide both sides by m:
k
15
=1⟹k=15