Question

Find the ratio of the following in the simplest form:
(i) $75$ paisa to $Rs.3$

(ii) $35$ minutes to $45$ minutes

(iii) $8kg$ to $400gm$

(iv) $48$ minutes to $1$ hour

(v) $2$ metres to $35$ cm

(vi) $35$ minutes to $45$ seconds

(vii) $2$ dozen to $3$ scores

(viii) $3$ weeks to $3$ days

(ix) $48$ min to $2$ hour $40$ min

(x) $3m5cm$ to $35cm$.

Answer 1

To take the ratio we will convert both the quantity in same units.

(i) $Rs.1$ $=100$ paise

[To convert rupees to paise, multiply rupees by $100$]

$\therefore$ $75$ paise : $Rs.3$ $=75:300=1:4$

(ii) $35$ minutes $:45$ minutes $=7:9$

(iii) $1kg=1000gm$

[To convert $kgtogm$, we have to multiply by 100]

$8kg:400gm=8000:400=20:1$

(iv) $1$ Hour $=60$ minutes

[To convert hour to minutes, we have to multiply hour by $60$]

$48$ minutes $:1$ hour $=48:60=4:5$

(v) $1$ metre $=100cm$

[To convert metre to cm, we have to multiply by metre to 100]

$2$ metres $:35cm=200:35=40:7$

(vi) $1$ minute $=60$ seconds.

$35$ minutes to $45$ seconds$=35\times 60:45=140:3$

(vii) $1$ dozen $=12$

$1$ score $=20$ or $3$ score $=3\times 20=60$

$2$ dozen: 3 scores $=24:60=2:5.$

(viii) $1$ week $=7$ days

[To convert week in days multiply by 7]

$3$ weeks $:3$ days $=21:3=7:1$

(ix) $1$ hour $=60$ minutes

$2$ hour $40$ minutes $=2\times 60+40=160$

$48$ min $:2$ hour $40$ minutes $=48:160=3:10$

(x) $1$ meter $=100cm$

$3m5cm=3\times 100+5=305cm$

$305$ minutes $:35$ minutes $=61:7$