Question

If a ratio b is equals to 3 ratio 7 and B ratio C is equals to 14 ratio 19 then find ABC

Answer 1

Question:

If the ratio of A & B is equal to 3:7 and the ratio of B & C is equal to 14:19, then find the combined ratio A:B:C .

Answer:

A:B:C = 6:14:19

Note:

• In a ratio, its first term is called antecedent and the second term is called consequent.

• If the simplest form of two or more ratios are same , then they are said to be equivalent ratios.

• Method to find combined ratio :

Step1 : Find the LCM of consequent of first ratio and antecedent of second ratio.

Step2 : Now make the equivalent ratios of both the given ratios such that the consequent of first ratio and the antecedent of second ratio are equal to the obtained LCM.

Step3 : Now finally combine both the ratios.

Solution:

It is given that ;

A:B = 3:7

B:C = 14:19

Let's find the combined ratio of A:B and B:C

(ie; A:B:C)

Step : 1

Here ,

The consequent (second term) of first ratio

(ie; A:B) is 7.

And the antecedent (first term) of second ratio

(ie; B:C) is 14.

Also , the LCM(7,14) = 14

Step : 2

Try to make the consequent of first ratio and antecedent of second ratio equal to there LCM.

Now,

=> A:B = 3:7

=> A:B = (3×2):(7×2)

=> A:B = 6:14

Also;

=> B:C = 14:19

=> B:C = (14×1):(19×1)

=> B:C = 14:19

Hence,

The obtained equivalent ratios are ;

A:B = 6:14 and B:C = 14:19

Step : 3

Now,

Combine the equivalent ratios A:B = 6:14 and

B:C = 14:19.

Hence,

The combined ratio will be ;

A:B:C = 6:14:19.

Hence,

Required ratio is ; A:B:C = 6:14:19

Answer 2

Given :----

• Ratio. of A : B = 3 : 7
• Ratio of B : C = 14 : 19

To Find :------

• A : B : C = ?

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$\Large\bold\star\underline{\underline\textbf{Solution(1)}}$

let A /B = 3x/7x ----------- Equation (1)

B/C = 14x/19x -------------- Equation (2)

Here, Value of B is different in both case ,

If we multiply A/B ratio of Equation (1) by 2, and Equation (2) by 1 , we get, same B .

so,

→ (3x * 2) / (7x * 2) = 6x/14x

→ (14x * 1) /(19x * 1) = 14x/19x ..

Hence, Ratio of all three will be :---- value of (A) : value of (B) that is common now : Value of (C)

$\large\boxed{\bold{A:B:C = 6:14:19}}$

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$\Large\bold\star\underline{\underline\textbf{Solution(2)}}$

$\red{\textbf{shortcut method}}$

Let, A :B = a : b and B : C = c : d ,

and we have to Find A : B : C ?

A : B : C will be :-----

$\large\boxed{\bold{a \times c:b \times c:b \times d}}$

Here in Question we have ,

A : B = 3 : 7 = a : b

B : C = 14 : 19 = c : d

Hence,

$A : B : C = 3 \times \cancel{14} : 14 \times \cancel 7 : \cancel7 \times 19 \\ \\ \red{\boxed\implies} \: \: A : B : C \: = 3 \times 2 : 14 \times 1 : 1 \times 19 \\ \\ \large\boxed{\bold{A : B : C = 6 : 14 : 19}}$

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$\large\underline\textbf{Hope it Helps You.}$