Are the following statements true?
(a) 40 persons : 200 persons $=$ 15 Rs : 75Rs
(b) 7.5 litres : 15 litres $=$ 5 kg : 10 kg
(c) 99 kg : 45 kg $=$ Rs. 44 : Rs. 20
(d) 32 m : 64 m $=$ 6 sec : 12 sec
(e) 45 km : 60 km $=$ 12 hours : 15 hours.

To do: 

We have to find whether the given statements are true.

Solution:

(a) $40\ persons: 200\ persons =Rs.\ 15: Rs.\ 75$

The ratio of  $40\ persons: 200\ persons $

$=\frac{40\ persons}{200\ persons}$

$=\frac{1}{5}$

The ratio of $Rs.\ 15: Rs.\ 75$

$=\frac{Rs.\ 15}{Rs.\ 75}$

$= \frac{1}{5}$

Since,

$40\ persons : 200\ persons = Rs.\ 15 : Rs.\ 75$

The given statement is True.

(b) $7.5\ litres : 15\ litres = 5\ kg : 10\ kg$

The ratio of $7.5\ litres: 15\ litres$

$=\frac{7.5\ litres }{15\ litres}$

$= \frac{1}{2}$

The ratio of $5\ kg: 10\ kg$

$=\frac{5\ kg}{10\ kg}$

$= \frac{1}{2}$

Since,

$7.5\ litres : 15\ litres = 5\ kg : 10\ kg$

The given statement is True.

(c) $99\ kg : 45\ kg = 44\ Rs : 20\ Rs$

The ratio of  $99\ kg: 45\ kg$

$=\frac{99\ kg}{45\ kg}$

$= \frac{11}{5}$

The ratio of $44\ Rs: 20\ Rs$

$=\frac{44\ Rs}{20\ Rs}$

$= \frac{11}{5}$

Since,

$99\ kg : 45\ kg = 44\ Rs : 20\ Rs$

The given statement is True.

(d) $32\ m : 64\ m = 6\ sec : 12\ sec$

The ratio of $32\ m: 64\ m$

$=\frac{32\ m}{64\ m}$

$= \frac{1}{2}$

The ratio of $6\ sec: 12\ sec$

$\frac{6\ sec}{12\ sec}$

$= \frac{1}{2}$

Since,

 $32\ m : 64\ m = 6\ sec : 12\ sec$

The given statement is True.

(e) $45\ km : 60\ km = 12\ hours : 15\ hours$

The ratio of  $45\ km: 60\ km$ 

$=\frac{45\ km}{60\ km}$

$= \frac{3}{4}$

The ratio of $12\ hours: 15\ hours$

 $=\frac{12\ hours}{15\ hours}$

$= \frac{4}{5}$

Since,

$45\ km: 60\ km ≠ 12\ hours: 15\ hours$

The given statement is False.

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Updated on: 10-Oct-2022

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