If a:b:c = 3:4:7 then ratio (a+b+c):c is equal to:

The correct answer is 2:1. When a ratio like a:b:c = 3:4:7 is given, it implies that the values of a, b, and c can be represented as multiples of a common factor, let's say 'x'. So, we can write a = 3x, b = 4x, and c = 7x. To find the ratio (a+b+c):c, we first calculate the sum a+b+c. Substituting the values, a+b+c = 3x + 4x + 7x = 14x. Now, we form the ratio (a+b+c):c, which becomes 14x:7x. To simplify this ratio, we divide both parts by the common factor, 7x. This results in 2:1, as 14x divided by 7x is 2, and 7x divided by 7x is 1.

• 14:3 is incorrect because this would imply that c is 3x, but according to the given ratio a:b:c = 3:4:7, c is actually 7x.
• 7:4 is incorrect. This ratio might result from incorrectly assuming a relationship like (a+b):c or from some other miscalculation. Based on the correct interpretation, (a+b+c):c simplifies to 2:1, not 7:4.
• 3:7 is incorrect because this is the ratio of 'a' to 'c' (a:c), not the ratio of the sum (a+b+c) to 'c'. The question specifically asks for (a+b+c):c.