Question

If A:B:C:D = 1/2:1/3:1/4:1/5, then find the value of (A + B) : (C+D)​

Answer 1

Step-by-step explanation:

take A and B

1/2+1/3= 3+2/6= 5/6 =A+B

now take C and D

1/4+1/5=5+4/20 = 9/20 =C+D

Now put in ratio form ,that is

A+B:C+D =5/6:9/20

Answer 2

Answer:

The required ratio is 50 : 27

Step-by-step explanation:

Given :

A : B : C : D = 1/2 : 1/3 : 1/4 : 1/5

To find :

the value of (A + B) : (C + D)

Solution :

$\tt A:B:C:D = \dfrac{1}{2} : \dfrac{1}{3} : \dfrac{1}{4} : \dfrac{1}{5}$

Multiply the ratio by a constant number, (say x)

Then,

A = (1/2)(x) = x/2

B = (1/3)(x) = x/3

C = (1/4)(x) = x/4

D = (1/5)(x) = x/5

Now,

(A + B) :

$\sf = \dfrac{x}{2} + \dfrac{x}{3} \\ \longrightarrow \tt LCM = 6 \\ \sf = \dfrac{x \times 3}{2 \times 3} + \dfrac{x \times 2}{3 \times 2} \\ \sf = \dfrac{3x}{6} + \dfrac{2x}{6} \\ \sf = \dfrac{3x+2x}{6} \\ \sf = \dfrac{5x}{6}$

(C + D) :

$\sf = \dfrac{x}{4} + \dfrac{x}{5} \\ \longrightarrow \tt LCM = 20 \\ \sf = \dfrac{x \times 5}{4 \times 5} + \dfrac{x \times 4}{5 \times 4} \\ \sf = \dfrac{5x}{20} + \dfrac{4x}{20} \\ \sf = \dfrac{5x+4x}{20} \\ \sf = \dfrac{9x}{20}$

Finding the value of (A + B) : (C + D)

= (A + B) : (C + D)

= (5x/6) : (9x/20)

= 5/6 : 9/20

= (5×20) : (6×9)

= 100 : 54

= 2(50) : 2(27)

= 50 : 27