Question

1. Find the ratio of the following:
a. 5 weeks to 65 days
b. 7 inches to 5 centimetres
c. 60 minutes to 6 hours
d. 500 cm to 16 metres
e. 7 kilograms to 800 grams
f. 76 to 4000 paise
g. 65 litres to 670 millilitres
h. 30 seconds to 45 minutes​

Answer 1

Given:-

• To find ratios of the given statements.

To find:-

• Ratio of "5 weeks to 65 days".

Solution:-

$1week = 7days \\ \\ \\ hence \: 5weeks = 5 \times 7 \\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: 35 \: days$

• 35:65

• $\small\bold\pink{Ratio=}$ $\small\bold\green{7:13}$

To find:-

• Ratio of 7 inches to 5cm

Solution:-

$1 \: inch = 5 \: cm \\ \\ 7 \: inches = 7 \times 5 \\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:= > 35 \: cm$

• 35:5

• $\small\bold\pink{Ratio=}$ $\small\bold\green{7:1}$

To find:-

• Ratio of 60 mins to 6 hrs.

Solution:-

• $1 \:hr = > 60 \: mins \\ \\ 6 \: hrs = > 6 \times 60 \\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = > 360 \: mins$
• =>60:360

• =>12:72

• $\small\bold\pink{Ratio=}$ $\small\bold\green{1:6}$

To find:-

• Ratio of 500 cm to 16 m

Solution:-

• $1m = 100 \: cm \\ \\ 16m = 16 \times 100m \\ \\ \: \: \: \: \: \: \: \: \: = > 1600 \: cm$
• =>500:1600

• =>100:320

• =>20:64

• $\small\bold\pink{Ratio=}$ $\small\bold\green{5:16}$

To find:-

• Ratio of 7 kg to 800 g

Solution:-

• $1 \: kg = 1000g \\ \\ 7kg = 7 \times 1000g \\ \\ \: \: \: = > 7000g$
• =>7000:800

• =>70:8

• $\small\bold\pink{Ratio=}$ $\small\bold\green{35:4}$

To find:-

• Ratio of ₹76:4000 Paise

Solution:-

• $1 \: rs = 100p \\ \\ 76rs = 76 \times 100p \\ \\ \: \: \: \: \: = > 7600p$
• =>7600:4000

• =>1900:1000

• =>475:250

• $\small\bold\pink{Ratio=}$ $\small\bold\green{19:10}$

To find:-

• Ratio of 65 Ls to 670 mls

Solution:-

• $1 \: l = 1000 \: mls \\ \\ 65l = 65 \times 1000 \: mls \\ \\ \: = > 6500mls$
• =>6500:670

• $\small\bold\pink{Ratio=}$ $\small\bold\green{650:67}$

To find:-

• Ratio of 30 secs to 45 mins.

Solution:-

• $1 \: mins = 60 \: secs \\ \\45mins = > 45 \times 60 \\ \\ \: \: \: \: \: \: \: \: = > 2700$
• =>30:2700

$\small\bold\pink{Ratio=}$ $\small\bold\green{1:90}$

Know more:-

A ratio must have same quantities.

if not then it must be converted to same quantities.

i.e., both sides of any ratio must be of same units.

A ratio is never mentioned in units such as g,kg,I,ml..

This is because both sides contain same units and get cancelled further.

a ratio is represented in form of p:q where the units of p and q are equal.

Hope it helped!

Answer 2

Given:-

• To find ratios of the given statements.

To find:-

• Ratio of "5 weeks to 65 days".

Solution:-

$1week = 7days \\ \\ \\ hence \: 5weeks = 5 \times 7 \\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: 35 \: days$

• 35:65

• $\small\bold\pink{Ratio=}$ $\small\bold\green{7:13}$

To find:-

• Ratio of 7 inches to 5cm

Solution:-

$1 \: inch = 5 \: cm \\ \\ 7 \: inches = 7 \times 5 \\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:= > 35 \: cm$

• 35:5

• $\small\bold\pink{Ratio=}$ $\small\bold\green{7:1}$

To find:-

• Ratio of 60 mins to 6 hrs.

Solution:-

• $1 \:hr = > 60 \: mins \\ \\ 6 \: hrs = > 6 \times 60 \\ \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = > 360 \: mins$
• =>60:360

• =>12:72

• $\small\bold\pink{Ratio=}$ $\small\bold\green{1:6}$

To find:-

• Ratio of 500 cm to 16 m

Solution:-

• $1m = 100 \: cm \\ \\ 16m = 16 \times 100m \\ \\ \: \: \: \: \: \: \: \: \: = > 1600 \: cm$
• =>500:1600

• =>100:320

• =>20:64

• $\small\bold\pink{Ratio=}$ $\small\bold\green{5:16}$

To find:-

• Ratio of 7 kg to 800 g

Solution:-

• $1 \: kg = 1000g \\ \\ 7kg = 7 \times 1000g \\ \\ \: \: \: = > 7000g$
• =>7000:800

• =>70:8

• $\small\bold\pink{Ratio=}$ $\small\bold\green{35:4}$

To find:-

• Ratio of ₹76:4000 Paise

Solution:-

• $1 \: rs = 100p \\ \\ 76rs = 76 \times 100p \\ \\ \: \: \: \: \: = > 7600p$
• =>7600:4000

• =>1900:1000

• =>475:250

• $\small\bold\pink{Ratio=}$ $\small\bold\green{19:10}$

To find:-

• Ratio of 65 Ls to 670 mls

Solution:-

• $1 \: l = 1000 \: mls \\ \\ 65l = 65 \times 1000 \: mls \\ \\ \: = > 6500mls$
• =>6500:670

• $\small\bold\pink{Ratio=}$ $\small\bold\green{650:67}$

To find:-

• Ratio of 30 secs to 45 mins.

Solution:-

• $1 \: mins = 60 \: secs \\ \\45mins = > 45 \times 60 \\ \\ \: \: \: \: \: \: \: \: = > 2700$
• =>30:2700

$\small\bold\pink{Ratio=}$ $\small\bold\green{1:90}$

Know more:-

A ratio must have same quantities.

if not then it must be converted to same quantities.

i.e., both sides of any ratio must be of same units.

A ratio is never mentioned in units such as g,kg,I,ml..

This is because both sides contain same units and get cancelled further.

a ratio is represented in form of p:q where the units of p and q are equal.

Hope it helped!