Question

Rs$324$ is divided among three friends Sonu, Monu and Hari in the ratio $5:6:7$. What is monu’s share of money?
A) $68$
B) $108$
C) $60$
D) $120$

Answer 1

Hint: We are given a certain amount of money that is to be divided among three friends in a certain ratio. We have to find the share of one friend with the help of the ratio. For the given ratio we will multiply the ratio by a same constant the value of ratio does not change. Then adding all the three values and equating to the total share given. Then we get the value of a constant we will find the required share of all three.

Complete step-by-step answer:
Step1: We are given a total share of $324$. It is divided among three friends i.e. Sonu, Monu and Hari the ratio is $5:6:7$.
Let us multiply the ratio by constant $x$
We get $5x,6x,7x$
Step2: Let $5x,6x,7x$ be the share of Sonu, Monu and Hari respectively. On adding the three shares and equating them to $324$
We get:
$\Rightarrow$$5x + 6x + 7x = 324$
$\Rightarrow$$18x = 324$
Dividing by $18$ we get
$\Rightarrow$$x = \dfrac{{324}}{{18}}$
$\Rightarrow$$x = 18$
Step 3: Substituting the value of $x$ in $5x,6x,7x$ we will get
Sonu’s share $ \Rightarrow 5 \times 18 = Rs90$
Monu’s share $ \Rightarrow 18 \times 6 = Rs108$
Hari’s share $ \Rightarrow 7 \times 18 = 126$

Option B is the correct answer.

Additional Information: If the ratio of the two numbers is a:b:c. Then the numbers can be assumed to be ak ,bk and ck where k is a constant. When all the elements of a ratio are multiplied or divided by the same number. The resulting ratio is equal to the original ratio

Note: Alternative method
Step1: Given ratio $5:6:7$
Total share $ = 324$
Adding the ratios
$5 + 6 + 7 = 18$
To find the share we use the formula
$share$=$\dfrac{{\text{Rate of that person share}} \times {\text{total share}}}{{\text{total ratio}}}$
Sonu’s share $ \Rightarrow \dfrac{5}{{18}} \times 324 = 90$
Monu’s share $ \Rightarrow \dfrac{6}{{18}} \times 32 = 108$
Hari’s share $ \Rightarrow \dfrac{7}{{18}} \times 32 = 126$