Question

What number should be added to the terms of 49:68 to get the ratio 3: 4?

Answer 1

Hint: A ratio is a number, which expresses one quantity as a fraction of the other. In this question, the number x is added to the given term in both numerator and denominator simultaneously.

Complete step-by-step answer:

A ratio is a mathematical term that is used to compare the size of one number to the size of another number. It is commonly used in mathematics. Ratios are usually shown as two or more numbers separated with a colon, for example, 8:5 or 1:4 or 3:2:1.
The given term is $\dfrac{49}{68}$ and let the number is to be added be x to get the ratio 3:4.
$\dfrac{49+x}{68+x}=\dfrac{3}{4}$
Taking the cross multiplication, we get
4(49+x) = 3(68+x)
Open the brackets, we get
196+ 4x = 204+3x
Rearranging the terms, we get
4x-3x = 204 – 196
x = 8
Hence x= 8 should be added to the terms of 49:68 to get the ratio 3:4.

Note: The possibility for the mistake is that you might get confused with the task is to find the number X which when added to the numbers a and b the ratio changes from a: b to c: d.
Approach: Old ratio is a : b and new ratio is c : d. Let the required number be X,
So, $\dfrac{a+X}{b+X}=\dfrac{c}{d}$ or ad + dX = bc + cX or X(d – c) = bc – ad. So, $X=\dfrac{(bc-ad)}{d-c}$.