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 $4\frac{1}{4}m$, find the number of such pieces.
[4 MARKS]

Answer 1

Each part: 2 Marks

(a) Distance of the first path taken for short cut $=\frac{4}{5}\times 10=8km$

Distance of the second path taken for short cut $=\frac{1}{3}\times 10=\frac{10}{3}km$

Total distance covered by Ram = $\frac{10}{3}+8=\frac{34}{3}km$

Difference in Distance $=\frac{34}{3}-10=\frac{4}{3}km$

Ram ended up covering a larger distance of 1.3 km.


(b) Let the number of pieces be $y$.

Length of one piece $=4\frac{1}{4}m$

Total length of y pieces = Total length of the rope

$4\frac{1}{4}\times y=68m$

$\frac{17}{4}\times y=68$

$y=\frac{68\times 4}{17}$

$=4\times 4$

$=16$

$\therefore$ 16 equal pieces of the given size can be cut.