Question

one piece of wire 14 by 15 m long broke into two pieces. one piece was 1 by 3 metre long how long was the other piece​

Answer 1

Answer:

9/15 m

$\rule{70mm}{2pt}$

Step-by-step explanation:

So we have a piece of wire that is 14/15 m long but that breaks into two pieces. The broken piece is 1/3 m long and asked to find the length of the other piece. The basic thing that could be done here is to subtract the broken piece of wire from the total length of the wire.

We don't know the length of the other piece of wire. So, let's call the other piece of wire be "x" m long.

As per given problem, we have total length of wire is 14/15 m (actual length of wire) and one of it's broken piece is 1/3 m long. We know that sum of two pieces of wire is the actual length of wire. So, we can say that, length of other or second piece of wire will be (14/15 - 1/3) m long.

Therefore,

$\underline{\boxed{\sf \purple{Total \: length \: of \: wire \: = \: Length \: of \: one \: piece \: + \: Length \: of \: other \: piece}}}$

Substitute the values,

$\purple{ \dashrightarrow} \: \sf{\dfrac{14}{15} \:=\:\dfrac{1}{3}\:+\: x}$

$\purple{ \dashrightarrow} \: \sf{\dfrac{14}{15} \:-\: \dfrac{1}{3}\:=\: x}$

Take L.C.M. or make the denominator same (to do so, multiply and divide the 1/3 by 5/5)

$\purple{ \dashrightarrow} \: \sf{\dfrac{14}{15} \: - \: \dfrac{1}{3} \: \times \: \dfrac{5}{5} \: = \: x}$

$\purple{ \dashrightarrow} \: \sf{\dfrac{14}{15} \: - \: \dfrac{5}{15}\: = \: x}$

Now, we have same denominator i.e. 15. So, simply do the rest calculations.

$\purple{ \dashrightarrow} \: \sf{\dfrac{14 \: - \: 5}{15}\: = \: x}$

$\purple{ \dashrightarrow} \: \sf{\dfrac{9}{15}\: = \: x}$

$\purple{\dashrightarrow}\:\boxed{\sf{x \: = \: \dfrac{9}{15}}}$

Therefore, length of other piece of wire = 9/15 m.

$\rule{70mm}{2pt}$

VERIFICATION:

From above calculations we have length of other (second) piece of wire is 9/15 m long and as per given question, legnth of wire is 14/15 m long & length of one piece is 1/3 m.

Length of wire = Length of one piece + Length of second (other) piece

→ 14/15 = 1/3 + 9/15

→ 14/15 = (5 + 9)/15

→ 14/15 = 14/15

Hence, proved.

Answer 2

207

wire = 14×15m =210

1st piece of wire = 1×3m = 3

:. 2nd piece of wire = 210 - 3 = 207

May this answer helps u