(Q) If a: b = 5: 9 and b: c = 7: 4, then find a: b: c ?

A) 24 : 43 : 56
B) 18 : 23 : 19
C) 35 : 63 : 36
D) 29 : 58 : 48

View Answer

C) 35 : 63 : 36

Explanation :
Here, we make the common term ‘b’ equal in both ratios.
Therefore, we multiply the first ratio by 7 and the second ratio by 9.
So, we have a : b = 35 : 63 and b : c = 63 : 36
Thus, a : b : c = 35 : 63 : 36

Formulas and Quick Tricks for Ratio and Proportion :
* Ratio of two quantities ‘a’ and ‘b’ having the same units is simply a / b and is usually written as a:b * The equivalence of two ratios is called proportion. If a: b = c : d, then a, b, c, d are said to be in proportion. Here, a x d = b x c * Mean proportional is the geometric mean. For example, the mean proportion of ‘a’ and ‘b’ is the square root of (a x b) * If we have two ratios, say a: b and c : d, then (a x c) : (b x d) is called the compounded ratio * If a: b = c : d, i.e., a/b = c/d, then (a + b) / (a – b) = (c + d) / (c – d) This is called Componendo and Dividendo * If we say that ‘a’ is directly proportional to ‘b’, it means that a = k x b, where ‘k’ is the constant of proportionality * If we say that ‘a’ is inversely proportional to ‘b’, it means that a = k / b or a x b = k, where ‘k’ is the constant of proportionality * If a ratio is multiplied or divided by a certain number, the properties of the ratio do not change. For example, if we multiply 1: 2 by 5, we get 5: 10, which is the same as 1: 2