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Hint: Given the ratio of income to the expenditure and the value of income, compute the value of expenditure. The value of savings is the difference between income and the expenditure.

Complete step-by-step answer:

Let the value of income be x and the value of expenditure be y.

The ratio of the income to the expenditure of the family is given as 7:6. Then, we have:

\[\dfrac{x}{y} = \dfrac{7}{6}............(1)\]

Now, it is given that the value of income is Rs.1400.

\[x = 1400...........(2)\]

We can find the value of expenditure by substituting equation (2) in equation (1).

\[\dfrac{{1400}}{y} = \dfrac{7}{6}\]

Solving for y, we get:

\[y = \dfrac{{1400 \times 6}}{7}\]

Simplifying further, we obtain:

\[y = 200 \times 6\]

\[y = 1200...........(3)\]

Hence, the value of expenditure is Rs.1200.

We now have the value of income and the expenditure. Hence, we can calculate the amount of savings of the family.

We know that,

Savings = Amount of Income – Amount of expenditure

Substituting equation (2) and equation (3) in the above equation, we get:

Savings = 1400 – 1200

Savings = 200

Therefore, the savings of the family is Rs.200.

Hence, the correct answer is Rs.200.

Note: You are required to have a basic knowledge that the amount of money remaining in the income after expenditure constitutes the savings. The ratio of income to the expenditure is greater than 1, hence you can cross check the answer since the savings should be positive.

Complete step-by-step answer:

Let the value of income be x and the value of expenditure be y.

The ratio of the income to the expenditure of the family is given as 7:6. Then, we have:

\[\dfrac{x}{y} = \dfrac{7}{6}............(1)\]

Now, it is given that the value of income is Rs.1400.

\[x = 1400...........(2)\]

We can find the value of expenditure by substituting equation (2) in equation (1).

\[\dfrac{{1400}}{y} = \dfrac{7}{6}\]

Solving for y, we get:

\[y = \dfrac{{1400 \times 6}}{7}\]

Simplifying further, we obtain:

\[y = 200 \times 6\]

\[y = 1200...........(3)\]

Hence, the value of expenditure is Rs.1200.

We now have the value of income and the expenditure. Hence, we can calculate the amount of savings of the family.

We know that,

Savings = Amount of Income – Amount of expenditure

Substituting equation (2) and equation (3) in the above equation, we get:

Savings = 1400 – 1200

Savings = 200

Therefore, the savings of the family is Rs.200.

Hence, the correct answer is Rs.200.

Note: You are required to have a basic knowledge that the amount of money remaining in the income after expenditure constitutes the savings. The ratio of income to the expenditure is greater than 1, hence you can cross check the answer since the savings should be positive.

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