Question

Four friends had a competition to see how far could they hop on one foot. The table given shows the distance covered by each.

Name	Distance covered (km)
Seema	`1/25`
Nancy	`1/32`
Megha	`1/40`
Soni	`1/20`

1. How farther did Soni hop than Nancy?
2. What is the total distance covered by Seema and Megha?
3. Who walked farther, Nancy or Megha?

Answer 1

We have, `1/25, 1/32, 1/40, 1/20`

First, we convert the numbers as like denominators.

Taking LCM of 25, 32, 40 and 20 = 2 × 2 × 2 × 5 × 5 × 4 = 800

we get

2	25, 32, 40, 20
2	25, 16, 20, 10
2	25,  8,  10,  5
5	25,  4,   5,   5
	5,   4,   1,   1

`1/25 = (1 xx 32)/(25 xx 32) = 32/800`,

`1/32 = (1 xx 25)/(32 xx 25) = 25/800`,

`1/40 = (1 xx 20)/(40 xx 20) = 20/800`

And `1/20 = (1 xx 40)/(20 xx 40) = 40/800`

a. Soni hop more than Nancy

= `40/800 - 25/800`

= `(40 - 25)/800`

= `15/800`

= `3/160` km

b. Total distance covered by Seema and Megha

= `32/800 + 20/800`

= `(32 + 20)/800`

= `52/800`

= `13/200` km

c. Clearly, Nancy walked farther than Megha.