[Solved] If a + b : b+c: c+ a = 2 : 3 : 5 and a + b + c = 20 then the value of c is: (a) 12 (c) 10 (b) 5 (d) 2

 If a + b : b + c : c + a = 2 : 3 : 5 and a + b + c
= 20, then the value of c is:

यदि a + b : b + c : c + a = 2 : 3 : 5 और a + b +
c = 20 है, तो c का मान है:

(a) 12             (b) 5
(c) 10             (d) 2
SSC GD 2022 TIER-1 

Solution :

Set up the Proportions:

We have the proportions:

a + b : b + c : c + a = 2 : 3 : 5

 

Solve for a, b, and c:

Let's represent the common factor in these proportions as 'x'. So we have:

a + b = 2x

b + c = 3x

c + a = 5x

We also know a + b + c = 20.

 

Let's substitute 'a + b' with '2x' and 'b + c' with '3x' in the equation a + b + c = 20:

2x + 3x = 20

5x = 20

x = 4

 

Now we can find the values of a, b, and c:

a + b = 2x = 8

b + c = 3x = 12

c + a = 5x = 20

 

Solving these simultaneously, we get:

a = 4

b = 4

c = 12

Answer: The value of c is 12. So the correct answer is (a).

 

 

Speed Math Solution (with explanation) : 

Given: $�+�:�+�:�+�=2:3:5$ $�+�+�=20$

We quickly find that $�=4$.

Then, $�=5�-(�+�)=5(4)-(2�)=20-8=12$.

So, the value of $�$ is 12.

 

Given that $�+�+�=20$ and the ratios $�+�:�+�:�+�=2:3:5$, 

you can observe that $�+�$ must be the largest sum because it has the highest ratio. So, $�+�=5�$, where $�$ is the common multiplier.

Since $�+�=20$, and the largest sum $�+�$ corresponds to 5x, which means $5�=20$, you can quickly deduce $�=4$.

Now, you directly know that $�=5�-�=5(4)-8=20-8=12$.

Therefore, you can determine that the value of $�$ is indeed 12 without explicitly calculating $�$ and $�$. This method allows you to solve the problem rapidly using mental math.