Question

3. The length of a rope is 100 m. If we cut two pieces of length 30 1/4 m and 42 1/5 m from it, find the length of the remaining rope.​

Answer 1

Answer:

The length of a rope is 100 m. If we cut two pieces of length 30 1/4 m and 42 1/5 m from it, find the length of the remaining rope.​

Step-by-step explanation:

The length of a rope = 100 m

1st piece                     = 30 1/4  =   121 / 4

2nd piece                   =  42 1/5  = 211 / 5

1st piece + 2nd piece =  121 / 4 + 211 / 5

                                   =    605 / 20 + 844 / 20

                                   =   1449 / 20

The length of the remaining rope = 100 - 1449 /20

                                                        = (2000 - 1449) / 20

                                                         =    551 / 20

                                                          =     270  11/20 m

Answer 2

Given data : The length of a rope is 100 m. If we cut two pieces of length 30 1/4 m and 42 1/5 m from it.

Solution : To find out, the length of the remaining rope :

➜ Total length of the rope = 100 m

Let, the rope cut into two part be x and y respectively.

Where, A = 30 1/4 m and B = 42 1/5 m.

Now,

➜ A = 30 1/4 m

➜ A = {(30 * 4) + 1}/4 m

➜ A = {120 + 1}/4 m

➜ A = 121/4 m

➜ A = 30.25 m ----{1}

Similarly,

➜ B = 42 1/5 m

➜ B = {(42 * 5) + 1}/5 m

➜ B = {210 + 1}/5 m

➜ B = {(42 * 5) + 1}/5 m

➜ B = 211/5 m

➜ B = 42.2 m ----{2}

Now, From eq. {1} and eq. {2}

➜ Length of two pieces = A + B

➜ Length of two pieces = 30.25 + 42.2

➜ Length of two pieces = 72.45 m ---{3}

Now,

➜ Length of remaining rope = Total length of the rope - Length of two pieces

➜ Length of remaining rope = 100 - 72.45

➜ Length of remaining rope = 27.55 m

Answer : Hence, remaining length of the rope is 27.55 m.

{Note : 1 m = 100 cm, So 27.55 m = {27.55 * 100} cm = 2755 cm}

{ To find the answer in a fraction :

Solution :

Total length of the rope = 100 m

Let, the rope cut into two part be x and y respectively.

Where, A = 30 1/4 m and B = 42 1/5 m.

Now,

➜ A = 30 1/4 m

➜ A = {(30 * 4) + 1}/4 m

➜ A = {120 + 1}/4 m

➜ A = 121/4 m ----{1}

Similarly,

➜ B = 42 1/5 m

➜ B = {(42 * 5) + 1}/5 m

➜ B = {210 + 1}/5 m

➜ B = 211/5 m ----{2}

Now, From eq. {1} and eq. {2}

➜ Length of two pieces = A + B

➜ Length of two pieces = 121/4 + 211/5

➜ Length of two pieces = (121 * 5)/(4 * 5) + (211 * 4)/(5 * 4)

➜ Length of two pieces = 605/20 + 844/20

➜ Length of two pieces = (605 + 844)/20

➜ Length of two pieces = 1449/20 m

Now,

➜ Length of remaining rope = Total length of the rope - Length of two pieces

➜ Length of remaining rope = 100 - 1449/20

➜ Length of remaining rope = {2000 - 1449}/20

➜ Length of remaining rope = 551/20 m

Answer : Hence, remaining length of the rope is 551/20 m.}