(a) Rahul's school is 10 km from his house. To cut the distance short he takes a shortcut. He first takes a route that is 4 5 of the original route but, he finds the road blocked at the end. The distance of his school from the blocked path is 1 3 of the original route. What was the difference in distance that Rahul covered by this new path and his original route? (b) From a rope 68m long, pieces of equal size are cut. If the length of one piece is 4 1 4 m , find the number of such pieces. [4 MARKS]

: Each part: 2 Marks (a) Distance of the first path taken for short cut = 4 5 × 10 = 8 k m Distance of the second path taken for short cut = 1 3 × 10 = 10 3 k m Total distance covered by Ram = 10 3 + 8 = 34 3 k m Difference in Distance = 34 3 − 10 = 4 3 k m Ram ended up covering a larger distance of 1.3 km. (b) Let the number of pieces be y . Length of one piece = 4 1 4 m Total length of y pieces = Total length of the rope 4 1 4 × y = 68 m 17 4 × y = 68 y = 68 × 4 17 = 4 × 4 = 16 ∴ 16 equal pieces of the given size can be cut.

(a) Rahul's school is 10 km from his house. To cut the distance short he ta

Question

(a) Rahul's school is 10 km from his house. To cut the distance short he takes a shortcut. He first takes a route that is

\frac{4}{5}

of the original route but, he finds the road blocked at the end. The distance of his school from the blocked path is

\frac{1}{3}

of the original route. What was the difference in distance that Rahul covered by this new path and his original route?
(b) From a rope 68m long, pieces of equal size are cut. If the length of one piece is