The ratio of the monthly income and expenditure of Dinesh is 17:14, and is monthly saving ₹1200. If his monthly income is increased by ₹10,000 and expenditure is decreased by ₹2,000, then the new ratio of his income and expenditure is:

Let Dinesh’s original monthly income be $$17k$$ rupees and his original monthly expenditure be $$14k$$ rupees, where $$k$$ is a positive constant common factor.

His monthly saving equals income minus expenditure:
$$\text{saving}=17k-14k=3k$$

The question states that his monthly saving is ₹12 000, so
$$3k = 12000 \;\;\Longrightarrow\;\; k = \frac{12000}{3}=4000$$

Therefore,

Original income $$=17k = 17\times4000 = \text{₹}68\,000$$
Original expenditure $$=14k = 14\times4000 = \text{₹}56\,000$$

Now apply the changes mentioned in the question:

New income $$= 68\,000 + 10\,000 = \text{₹}78\,000$$
New expenditure $$= 56\,000 - 2\,000 = \text{₹}54\,000$$

Hence the new ratio of income to expenditure is
$$78\,000 : 54\,000$$

Divide both terms by their highest common factor, ₹6 000:

$$\frac{78\,000}{6\,000} : \frac{54\,000}{6\,000} = 13 : 9$$

Thus the required ratio is $$13:9$$.

Option B which is: 13:9