Question

Let 2a=3b=5c . (a)Find the ratio a : b : c . (b)If a-b+c=55, find c.

Answer 1

Answer:

2a =3b = 5c

let, 2a=3b =5c = k

∴ 2a = k ⇒ a = k/2

3b = k ⇒ b = k/3

5c = k ⇒ c = k/5

∴ a : b : c = k/2:k/3:k/5

= 1/2:1/3:1/5

The LCM of 2, 3 and 5 is 30.

Multiplying numerator by 30, we get

30/2:30/3:30/5

=15:10:6

Hence, a : b : c =15 : 10 : 6.

Answer 2

Answer:

a)A:B:C=15:10:6

b)c=30

Step-by-step explanation:

2A=3B=5C  

Taking the LCM of 2,3 & 5, we get 30.

Therefore,

$30A/15=30B/10=30C/6$

Dividing all by 30, we get,

$A/15=B/10=C/6=k (say)$

A/15=k ---------------------------(1)

=>A=15k

B/10=k ----------------------------(2)

=>B=10k

C/6=k -----------------------------(3)

=>C=6k

Now,

A:B:C=15k:10k:6k

Removing k,

A:B:C=15:10:6

B)    a-b+c=55-----------------------------(4)

through 1 and 2

2a=5c

so a=5c/2

through 2 and 3

6b=10c

so b=5c/3

put value of a and b in (4)

5c/2-5c/3+c=55

(15c-10c+6c)/6 = 55

11c/6=55

c=30