Question

If a + b:a- b = 7:5 find the ratio b:a​

Answer 1

Answer:

1:6

Step-by-step explanation:

a+b:a-b=7:5

5(a+b)=7(a-b)

12b=2a

b:a=1:6

Answer 2

Step-by-step explanation:

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Asked on January 17, 2020 by

Rekha Tirumala

If a:(b+c)=1:3 and c:(a+b)=5:7 then b:(a+c) is equal to

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ANSWER

It is given that a:(b+c)=1:3 and c:(a+b)=5:7 and we solve these expressions as follows:

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.