Question

1. A rope of length 3 meters 60 centimeters is cut into 2 pixes such that the ratio of the length of the pieces is 7:5. Find the length of the larger piece.
2. 80 kg of rice is packed into 2 bags in the ratio 9:7. Find the the weight of rice in the lighter bag. ​

Answer 1

Solutions!!

(1)

Length of rope = 3 m 60 cm

Converting the units.

1 m = 100 cm

3 m = 300 cm

Length of rope = 300 cm + 60 cm

Length of rope = 360 cm

The rope is cut in two pieces such that the ratio of the length of the pieces is 7:5.

Let it be 7x and 5x.

7x + 5x = 360

12x = 360

x = 30 cm

7x = 7 × 30 cm = 210 cm

5x = 5 × 30 cm = 150 cm

Length of the larger piece of rope is 210 cm.

(2)

80 kg rice packed in 2 bags in a ratio 9:7.

Let the weights be 9x and 7x.

9x + 7x = 80

16x = 80

x = 5

9x = 9 × 5 kg = 45 kg

7x = 7 × 5 kg = 35 kg

Hence, the weight of the lighter bag is 35 kg.

Answer 2

Answer:

SOLUTION NO 1 :-

Given :-

• A rope of length 3 m 60 cm is cut into 2 pieces such that the ratio of the length of the pieces is 7 : 5.

To Find :-

• What is the length of the larger piece.

Solution :-

First we have to convert the units m into cm :

$\implies \sf Length_{(Rope)} =\: 3\: m$

$\implies \sf Length_{(Rope)} =\: (3 \times 100)\: cm$

$\implies \bf Length_{(Rope)} =\: 300\: cm$

Now,

$\bigstar$ A rope of length 300 cm 60 cm.

$\leadsto \sf Total\: Length =\: 300\: cm + 60\: cm$

$\leadsto \sf Total\: Length =\: (300 + 60)\: cm$

$\leadsto \sf\bold{\green{Total\: Length =\: 360\: cm}}$

Again,

$\bigstar$ A rope whose total length is 360 and it is cut into 2 pieces such that the ratio of the length of the pieces is 7 : 5.

Let,

$\mapsto \bf Larger\: Piece_{(Rope)} =\: 7a\: cm$

$\mapsto \bf Smaller\: Piece_{(Rope)} =\: 5a\: cm$

According to the question,

$\footnotesize \implies \sf \bigg\{Larger\: Piece_{(Rope)}\bigg\} + \bigg\{Smaller\: Piece_{(Rope)}\bigg\} =\: 360$

$\implies \sf 7a + 5a =\: 360$

$\implies \sf 12a =\: 360$

$\implies \sf a =\: \dfrac{\cancel{360}}{\cancel{12}}$

$\implies \sf\bold{\purple{a =\: 30}}$

Hence, the required pieces are :

✯ Larger Piece Of Rope :

➳ Larger Piece = 7a

➳ Larger Piece = 7(30)

➳ Larger Piece = 7 × 30

➳ Larger Piece = 210 cm

✯ Smaller Piece Of Rope :

➳ Smaller Piece = 5a

➳ Smaller Piece = 5(30)

➳ Smaller Piece = 5 × 30

➳ Smaller Piece = 150 cm

$\therefore$ The length of the larger piece is 210 cm .

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SOLUTION NO 2 :-

Given :

• 80 kg of rice is packed into 2 bags in the ratio of 9 : 7.

To Find :-

• What is the weight of rice in the lighter bag.

Solution :-

Let,

$\leadsto \bf Heavy\: Weight\: Bag =\: 9a$

$\leadsto \bf Light\: Weight\: Bag =\: 7a$

According to the question,

$\bigstar$ 80 kg of rice is packed into 2 bags in the ratio of 9 : 7.

$\footnotesize \implies \bf \bigg\{Heavy\: Weight\: Bag\bigg\} + \bigg\{Light\: Weight\: Bag\bigg\} =\: 80$

$\implies \sf 9a + 7a =\: 80$

$\implies \sf 16a =\: 80$

$\implies \sf a =\: \dfrac{\cancel{80}}{\cancel{16}}$

$\implies \sf\bold{\purple{a =\: 5}}$

Hence, the required weight of rice :

✯ Heavy Weight Bag :

➸ Heavy Weight Bag = 9a

➸ Heavy Weight Bag = 9(5)

➸ Heavy Weight Bag = 9 × 5

➸ Heavy Weight Bag = 45

✯ Light Bag :

➸ Light Weight Bag = 7a

➸ Light Weight Bag = 7(5)

➸ Light Weight Bag = 7 × 5

➸ Light Weight Bag = 35

$\therefore$ The weight of rice is in the lighter bag is 35 kg .