Question

Rs.750 is divided among A, B, and C in such a manner that \[A:B = 5:2\]and\[B:C = 7:13\]. What is A’s share?
A)Rs.350
B)Rs.260
C)Rs.140
D)Rs.250

Answer 1

Hint: Ratio is a quantitative relation between two amounts, which shows the number of times one value contains with the other. It is a way to compare two quantities by using the division method, where a mile per hour is a comparison of miles and hours. It is a mathematical expression written in the form a: b, where a and b be any integers.
Proportion is an equation that says that two ratios are equivalent. Two varying quantities can be said in proportion if their multiple is connected to a constant; that is when either their ratio or proportion yields a constant.
In this question, the ratio of proportionality is given for three quantities, hence first find how those three quantities are proportional by using cross multiplication and then find the numbers.

Complete step-by-step solution
Given the amount is to be divided into three parts A, B, and C, where
\[A:B = 5:2\]
\[B:C = 7:13\]
Since B is common in both the ratios by using cross multiplying the values of B’s find then ratio of A:B:C by
\[\Rightarrow\dfrac{A}{B} = \dfrac{{5 \times 7}}{{2 \times 7}} = \dfrac{{35}}{{14}}\]
\[\Rightarrow\dfrac{B}{C} = \dfrac{{7 \times 2}}{{13 \times 2}} = \dfrac{{14}}{{26}}\]
Now the value of B in both the ratios is the same; hence it can be written as \[A:B:C = 35:14:26\]
Now, let the assume
A’s share= 35x
B’s share= 14x
C’s share=26x
Since Rs.750 is to be divided among A, B, and C, it can be written
\[
 \Rightarrow 35x + 14x + 26x = 750 \\
  \Rightarrow 75x = 750 \\
 \Rightarrow x = 10 \\
 \]
Hence the share of A’s =\[x = 35 \times 10 = Rs.350\]

Thus the correct answer is option (A).

Note: Students get confused when the ratios of the three variables are given in two different ratios. To solve these questions, find the common multiple of the two ratios and then solve for the ratio of three quantities.