Question

a man spends one-third of his income on rent. one-fifth on food,one-tenth on health of his family and remaining of which rs 462 on commodities.find his total income.

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Answer 1

Given : Income spent on Rent = 1/3

Income spent on Food = 1/5

Income spent on Health = 1/10

To Find: The total income

Solution:

Let the total income of the person be = x

Thus,

On Rent = x/3  

On Food = x/5

On Health = x/10

Combined Income -

x/3 + x/5 + x/10 + 462 = x

(10x + 6x + 3x )/30 + 462 = x

462 = x- 19x/30

462 = (30X - 19X) / 30

x = (462 × 30 ) / 11

x = 1260

Answer: The total income of the person is Rs. 1260

Answer 2

Given:

The fraction of the total income that the man spends:

On rent: $\frac{1}{3}$

On food: $\frac{1}{5}$

On health: $\frac{1}{10}$

On commodities: Rs. 462

To find:

The man's total income

Solution:

Let Rs. "x" be the total income of the man.

The given fractions of the man's total income is spent on rent, food and health, so

The remaining fraction of the total income which is spent on commodities is given by,

= 1 - [$\frac{1}{3} + \frac{1}{5}+\frac{1}{10}$]

= 1 - $\frac{10+6+3}{30}$

= 1 - $\frac{19}{30}$

= $\frac{30-19}{30}$

= $\frac{11}{30}$

But, Rs. 462 was spent on commodities

∴ $\frac{11}{30}$ * x = 462

⇒ x = $\frac{462 \:* \:30}{11}$

⇒ x = $\frac{13860}{11}$

⇒ x = Rs. 1260

Thus, the man's total income is Rs. 1260.

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