Question

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

Answer 1

(a) 40 persons: 200 persons = $₹15: ₹ 75$
$= \frac{40}{200} = \frac{1}{5} = 1:5$

$₹ 15: ₹ 75 = \frac{15}{75}$
$=\frac{ 1}{5}$
$= 1:5$
Since, 40 persons: 200 persons $= ₹ 15 : ₹ 75$
Hence, the statement is true.

---

(b) 7.5 litres : 15 litres = 5kg: 10kg
$=\frac{ 7.5}{15} = \frac{75}{150}$

$= \frac{1}{2} = 1:2$
5 kg: 10 kg = $\frac{5}{10}$
$= \frac{1}{2} = 1:2$
Since, 7.5 liters: 15 liters = 5 kg: 10 kg
Hence, the statement is true.

---

(c) 99 kg: 45kg = $₹44 :₹20$
$= \frac{99}{45} = \frac{11}{5}$
$= 11:5$
$₹ 44 : ₹ 20 = \frac{44}{20}$
$= \frac{11}{5} = 11:5$
Since, 99 kg: 45 kg$= ₹ 44 : ₹ 20$
Hence, the statement is true.

---

(d) 32m: 64m=6sec: 12 sec
$= \frac{32}{64} = \frac{1}{2} = 1:2$

6 sec: 12 sec =$\frac{ 6}{12}$
$= \frac{1}{2} = 1:2$
Since, 32 m: 64 m = 6 sec: 12 sec
Hence, the statement is true.

---

** (e)** 45km: 60km = 12hours: 15 hours
$= \frac{45}{60} = \frac{3}{4} = 3:4$

12 hours: 15 hours $= \frac{12}{15} =\frac{ 4}{5} = 4:5$
Since, 45 km: 60 km $≠$ 12 hours : 15 hours
Hence, the statement is false.

So, the answers is: (a) True (b) True (c) True (d) True (e) False