Question

A sum of rs. 430 has been distributed among 45 people consisting of men, women and children. The total amount given to men, women and children are in the ratio 12 : 15 : 16. But, the amounts received by each man, woman and child are in the ratio 6 : 5 : 4. Find, what each man, woman and child receives (in rs.)

Answer 1

6:10:12 we shall subtract them because they ask the how the man ,women and child receive

Answer 2

The amount received by each men is '6b' = ₹12

The amount received by each women is '5b'= ₹10

The amount received by each men is '4b' = ₹8

Step-by-step explanation:

Let the number of men is x.

Let the number of women is y.

Let the number of child is z.

Given:

• A sum of rs. 430 has been distributed among 45 people consisting of men, women and children.

$\rightarrow \: x + y + z = 45 \: .............(1)$

• The total amount given to men, women and children are in the ratio 12 : 15 : 16.

Let the common ratio of men, women and children in total amount is a.

$\rightarrow \: 12a + 15a + 16a = 430 \\ \rightarrow \: 43a = 430 \\ \rightarrow \: a = 10$

The total amount given to men = 12a = ₹120.

The total amount given to women=15a= ₹150.

The total amount given to children= 16a= ₹160.

• The amounts received by each man, woman and child are in the ratio 6 : 5 : 4.

Let the common ratio of the amount received by each men, women and children is b.

The amount received by each men is given by

$\rightarrow \: 6b = \frac{120}{x} \\ \rightarrow \: x = \frac{20}{b}$

The amount received by each women is given by

$\rightarrow \: 5b = \frac{150}{y} \\ \rightarrow \:y = \frac{30}{b}$

The amount received by each children is given by

$\rightarrow \: 4b = \frac{160}{z} \\ \rightarrow \: z = \frac{40}{b}$

Put value of x ,y and z in equation (1) is given by

$\rightarrow \: x + y + z = 45 \\ \rightarrow \: \frac{20}{b} + \frac{30}{b} + \frac{40}{b} = 45 \\ \rightarrow \:\frac{90}{b} = 45 \\ \rightarrow \: b = 2$

The amount received by each men is '6b' = ₹12

The amount received by each men is '6b' = ₹12The amount received by each women is '5b'= ₹10

The amount received by each men is '6b' = ₹12The amount received by each women is '5b'= ₹10The amount received by each men is '4b' = ₹8