If the cost of $6\dfrac{1}{4}$ m of cloth is ₹$1421\dfrac{7}{8}$, then find the cost of 1 metre of cloth.

Given:

Total cost = ₹$1421\dfrac{7}{8} = ₹\dfrac{11375}{8}$

Total length = $6\dfrac{1}{4}\text{ m} = \dfrac{25}{4}\text{ m}$

Cost of 1 metre of cloth = ?

Cost of 1 metre of cloth = (Total cost) ÷ (Total length)

Substituting the values in above, we get:

Cost of 1 metre of cloth = ₹ $\dfrac{11375}{8} ÷ \dfrac{25}{4}$ m

$\begin{array}{ll} = ₹\Big(\dfrac{11375}{8} \times \dfrac{4}{25}\Big) & [\text{Reciprocal of } \dfrac{25}{4} \text{ is } \dfrac{4}{25}] \\ = ₹\Big(\dfrac{455}{8} \times \dfrac{4}{1}\Big) & \text{[Simplifying 11375 and 25 ⇒ Divide by 25]} \\ = ₹\Big(\dfrac{455}{2} \times \dfrac{1}{1}\Big) & \text{[Simplifying 4 and 8 ⇒ Divide by 4]} \\ = ₹\dfrac{455 \times 1}{2 \times 1} \\ = ₹\dfrac{455}{2} \\ = ₹227\dfrac{1}{2} \end{array}$

∴ The cost of 1 metre of cloth = ₹$227\dfrac{1}{2}$