Divide ₹ 1870 into three parts in such a way that half of the first part, one-third of the second part and one-sixth of the third part are all equal.

Let half of the first part, one-third of the second part and one-sixth of the third part be equal to x.

⇒ $\dfrac{1}{2}$ First part = x

⇒ First part = 2x

⇒ $\dfrac{1}{3}$ Second part = x

⇒ Second part = 3x

⇒ $\dfrac{1}{6}$ Third part = x

⇒ Third part = 6x.

We know that,

⇒ Total = ₹ 1870

⇒ 2x + 3x + 6x = ₹ 1870

⇒ 11x = ₹ 1870

⇒ x = $\dfrac{1870}{11}$ = ₹ 170.

First part = 2x = 2 × 170 = ₹ 340

Second part = 3x = 3 × 170 = ₹ 510

Third part = 6x = 6 × 170 = ₹ 1020

Hence, first part = ₹ 340, second part = ₹ 510 and third part = ₹ 1020.