Answer: Correct option is A)
It is given that a:(b+c)=1:3 and c:(a+b)=5:7 and we solve these expressions
Step-by-step explanation:
b+c
a
=
3
1
⇒3a=b+c
⇒3a−b=c....(1)
a+b
c
=
7
5
⇒7c=5(a+b)
⇒7c=5a+5b....(2)
Multiplying the first equation by 7 we get:
7(3a−b)=7c
⇒7c=21a−7b....(3)
Now, subtracting equation 2 from equation 3, we have:
7c−7c=(21a−7b)−(5a+5b)
⇒0=21a−7b−5a−5b
⇒16a=12b
⇒b=
12
16a
⇒b=
3
4a
Substituting the value of b in equation 1:
3a−
3
4a
=c
⇒c=
3
9a
−
3
4a
⇒c=
3
9a−4a
⇒c=
3
5a
Now, lets find the value of b:(a+c) as shown below:
a+c
b
=
a+
3
5a
3
4a
=
3
3a
+
3
5a
3
4a
=
3
8a
3
4a
=
3
4a
×
8a
3
=
8a
4a
=
2
1
=1:2
hence, b:(a+c)=1:2.
