Question

A & B share a cost in the ratio \[7:2\]. A pays \[pounds126\], how much does B pays?

Answer 1

Hint: A ratio is a comparison of two numbers, separated by a colon sign. A ratio indicates how much one quantity is as compared to the other. In this case, in ratio of A and B, A is more than B. Also, the ratio signifies the parts, so if there are two parts, the sum of these two should make up the entire quantity. If there would have been three quantities like A, B and c, the sum these three would return the complete quantity.

Complete step by step solution:
The total sum of these two parts will be \[7 + 2 = 9\]
These \[7\] parts represent the entire quantity. Out of these parts, A pays \[7\] parts but it is given in the question that A pays \[pounds126\] i.e.\[7\] parts correspond to \[pounds126\].
If \[7\] parts equal \[pounds126\], so, one part will be equivalent to \[pounds126 \div 7 = \,pounds18\]
Also, it is given that B pays \[2\] parts.
Since, we now know the how much amount one part contain, we can easily calculate the value of \[2\] parts
We will simply multiply the value one part with \[2\].
\[ \Rightarrow pounds18 \times 2 = pounds36\]

Therefore, B pays an amount of \[pounds36\]

Note: Ratios can also be considered as fraction. The value before the colon will be the numerator and the value after the colon will be the denominator of the fraction. Using this concept of ratios of fraction, there is an alternative approach to this question.
In the question it is given that A pays \[pounds126\] , the ratio of the amount paid by A and B is also given, which corresponds to A pays \[7\] parts. Hence, \[7\] parts should correspond to \[pounds126\]
This situation can be mathematically written as-
\[\dfrac{{{\text{Parts}}\,{\text{of}}\,{\text{A}}}}{{{\text{Parts}}\,{\text{of}}\,{\text{B}}}}{\text{ = }}\dfrac{{\text{7}}}{{\text{2}}}{\text{ = }}\dfrac{{{\text{pounds126}}}}{{\text{B}}}\]
\[ \Rightarrow \dfrac{7}{2} = \dfrac{{pounds 126}}{B}\]
This can be further simplified by cross multiplication,
\[ \Rightarrow 7B = 2 \times pounds126\]
\[ \Rightarrow 7B = pounds252\]
Dividing both sides by\[7\], we get
\[ \Rightarrow B = \dfrac{{pounds252}}{7}\]
Let us divide the term and we get,
\[ \Rightarrow B = pounds36\]
Therefore, B has to pay \[pounds36\]