Question

A rope of length 3 m 60 cm is cut into two pieces such that the ratio of the lengths of the pieces is 7:5 . Find the length of the larger piece.​ ​

Answer 1

Answer :-

Length of larger piece = 210 cm

$\rule{100}2$

Length of rope is 3 m 60 cm.

→ (300 + 60) cm

→ 360 cm.

So, we have a rope whose length is 360 cm which is cut into two pieces such that the ratio of the pieces is 7:5.

We have to find a larger piece of rope.

Let the -

• larger piece of rope be 7M
• smaller piece of rope be 5M

Smaller piece of rope + Larger piece of role = Length of rope

Substitute the known values above

→ 5M + 7M = 360

→ 12M = 360

→ M = 360/12

→ M = 30

$\therefore$ Larger piece of rope = 7(30)

→ 210 cm

$\therefore$ Smaller piece of rope = 5(30)

→ 150 cm

____________________________

Verification :-

From above calculations -

• larger piece of rope = 210 cm
• smaller piece of rope = 150 cm

Smaller piece of rope + Larger piece of rope = Length of rope

=> 150 + 210 = 360

=> 360 = 360

Answer 2

GIVEN:-

LENGTH OF ROPE =3m 60cm

=>360cm.

NOW, THE RATIO OF THEIR LENGTH=7:5

SO LET US ASSUME THE LENGTH'S REQUIRED BE AS 'k'.

THEN,RATIO =7k+5k

SUM OF THE RATIO'S=7k+5k=12k

A/Q,

7k+5k=360

=>12k=360

=>k=30.

PUTTING THE VALUES OF k WE GET,

▪7k=7×30=210.

▪5k=5×30=150.

CLEARLY, 210 IS LARGER THAN 150 SO,THE LARGER PIECE IS 210.