Question

Complete the following table.

S.No.	First quantity	Second quantity	Ratio	Simplified ratio
1.	20 paisa	Rs 1
2.	800 g	1 kg
3.	1 hr	30 min
4.	2 m	125 cm
5.	3 min	45 sec
6.	30 mm	1 cm

Answer 1

Hint: Here, we are required to complete the given table. So, we will use various conversion formulas and the relationship between various quantities and units. We will use this to represent the respective quantities to make the units of the quantities same and hence, find the required ratio and the simplified ratio.

Complete step-by-step answer:
In order to complete the given table, we will use the conversion formulas.
As we now,
1. Rs 1$ = 100$paisa
Hence, for the first part, we will simply substitute this value to make the units of both the quantities same.
Thus, the ratio obtained will be: $20:100$
Now, writing this ratio in fractional form and then further simplifying it by dividing the numerator and denominator by 20, we get,
$20:100 = \dfrac{{20}}{{100}} = \dfrac{1}{5}$
Therefore, the simplified ratio obtained is $1:5$
Hence, this is the required answer for the first part.
2. Similarly, substituting 1 kg$ = 1000$g in the second quantity of second part, we get the ratio as $800:1000$
Now, dividing the numerator and denominator of the fractional form of this ratio by 200, we get,
$800:1000 = \dfrac{{800}}{{1000}} = \dfrac{4}{5}$
Therefore, the required simplified ratio is $4:5$
3. Here, substituting 1 hr$ = 60$min in the first quantity, we get the ratio as $60:30$
Now, dividing the numerator and denominator of the fractional form of this ratio by 30, we get,
$60:30 = \dfrac{{60}}{{30}} = \dfrac{2}{1}$
Therefore, the required simplified ratio is $2:1$
4. We know that, 1 m$ = 100$cm.
Hence, multiplying both sides by 2, we get,
2m$ = 200$cm
Substituting this in the first quantity, we get the ratio as $200:125$
Now, dividing the numerator and denominator of the fractional form of this ratio by 25, we get,
$200:125 = \dfrac{{200}}{{125}} = \dfrac{8}{5}$
Therefore, the required simplified ratio is $8:5$
5. We know that, 1 min$ = 60$sec
Hence, multiplying both sides by 3, we get,
3 min$ = 180$sec
Substituting this in the first quantity, we get the ratio as $180:45$
Now, dividing the numerator and denominator of the fractional form of this ratio by 45, we get,
$180:45 = \dfrac{{180}}{{45}} = \dfrac{4}{1}$
Therefore, the required simplified ratio is $4:1$
6. We know that, 1 cm$ = 10$mm
Hence, substituting this in the second quantity, we get the ratio as $30:10$
Now, dividing the numerator and denominator of the fractional form of this ratio by 10, we get,
$30:10 = \dfrac{{30}}{{10}} = \dfrac{3}{1}$

Therefore, the required simplified ratio is $3:1$

Hence, this is the required complete table:

S.No.	First quantity	Second quantity	Ratio	Simplified ratio
1.	20 paisa	Rs 1	$20:100$	$1:5$
2.	800 g	1 kg	$800:1000$	$4:5$
3.	1 hr	30 min	$60:30$	$2:1$
4.	2 m	125 cm	$200:125$	$8:5$
5.	3 min	45 sec	$180:45$	$4:1$
6.	30 mm	1 cm	$30:10$	$3:1$

Note:
Coins in India are issued in denominations of 50 paisa, one rupee, two rupees, five rupees, and ten rupees. A paisa is ${\dfrac{1}{{100}}^{th}}$ of a rupee. Quantities can be measured using either kilograms or grams and in order to measure distance between two points or places, we use the units like meters, centimetres and millimetres. Also, last but not the least; time can be measured in hours, minutes or seconds. Thus, the relation between these units is really important in day-to-day life.