Question

. A piece of cloth 3/4 m long was cut into three pieces. The first piece was 3/20 m long, while the length of the second piece was 4/3 of the first. How long was the third piece?

5/3 m

2/5 m

7/20 m

6/13 m​

Answer 1

Second Option

Step-by-step explanation:

Given:-

A piece of cloth 3/4 m long was cut into three pieces. The first piece was 3/20 m long, while the length of the second piece was 4/3 of the first.

To find:-

How long was the third piece?

Solution:-

Given that

The length of the cloth = 3/4 m

It is cut into 3 pieces

Length of the first piece = 3/20 m

Length of the second piece = 4/3 of the first piece

=>(4/3)×(3/20)

=> (4×3)/(3×20)

=>12/60

=> 1/5 m

Length of the second piece = 1/5 m

Let the length of third piece be X m

Total length of the cloth

= First piece + Second piece + Third piece

=> (3/20) + (1/5) + X = 3/4

LCM of 20 and 5 = 20

=> (3+4+20X)/20 = 3/4

=> (7+20X)/20 = 3/4

=> 7+20X = (3/4)×20

=>7+20X = (3×20)/4

=>7+20X = 60/4

=>7+20X=15

=>20X = 15-7

=>20X = 8

=>X=8/20

=>X=2/5 m

Therefore, X = 2/5 m

Answer:-

Length of the third piece of the cloth = 2/5 m

Check:-

Length of the cloth

=(3/20)+(1/5)+(2/5)

=(3+4+8)/20

=15/20

=3/4 m

Length of the cloth = 3/4 m

Verified the given relation.