Question

if a:b=2:3;b:c=6:5 and a+b+c=30 and then 2a+3b+4c=?

Answer 1

SOLUTION:
a: b = 2: 3, b: c = 6: 5
a/b = ⅔ , b/c = 6/5
In the ratio a: b , b = 3 and in the ratio b:c , b=6. We have to make b equal in the two ratios. LCM of 3 and 6 = 3×6. So we multiply the antecedent and consequent of the first ratio by 6 and antecedent and consequent of 2nd ratio by 3
a: b = 2:3 = (2×6) : (3×6) = 12:18
b:c = 6:5 =(6×3) : (5×3)= 18 : 15
Then, a: b: c = 12: 18: 15
a: b: c = 4: 6: 5
Let a, b and c be 4 x, 6 x & 5 x
a + b + c = 30 (Given)
Then, 4 x + 6 x+ 5 x = 30
15 x= 30
x = 30/15
x = 2
The value of a = 4x=4 x 2 = 8, b = 6x=6 x 2= 12 & c =5x = 5 x 2 = 10.
So, the value of 2a + 3b + 4c
= 8 x 2 + 12 x 3 + 4 x 10
= 16 + 36 + 40
= 92.
Hence, the value of 2a+ 3b +4c =92.

Answer 2

Answer:

Given,

A : B = 2 : 3

B : C = 6 : 5

A + B + C = 30

Let's find the values of A, B and C

We can observe,

The value of B is different in both the ratios.

So, we need to find the LCM of values of B

LCM (3, 6) = 6

To make the value of B equal in both the ratios,

We have multiply A : B ratio by 2.

(A : B) × 2

2 × 2 : 3 × 2

4 : 6

B : C

6 : 5

Now, value of B is equal in both the ratios.

Therefore,

A : B : C

4 : 6 : 5

A + B + C = 30

4x + 6x + 5x = 30

15x = 30

x = 30 / 15

x = 2

A ⟾ 4x ⟾ 4 × 2 = 8

B ⟾ 6x ⟾ 6 × 2 = 12

C ⟾ 5x ⟾ 5 × 2 = 10

A + B + C = 30

8 + 12 + 10 = 30

30 = 30

2A + 3B + 4C

= (2 × 8) + (3 × 12) + (4 × 10)

= 16 + 36 + 40

= 92