Selina Concise Class 6 Math Chapter 12 PROPORTION (including Word Problems) Exercise 12C Solution
EXERCISE 12C
(1) Are the following numbers in proportion?
(i) 32 × 60 = 40 × 48
⇒ 1920 = 1920
So, it is true.
(ii) 12 × 20 = 15 × 18
⇒ 240 ≠ 270
So, it is false.
(2) Find the value of x in each of the following such that the given numbers are in proportion.
(i) 42x = 75 × 14
⇒ x = 1050/42
⇒ x = 25
(ii) 45x = 135 × 90
⇒ x = 12150/45
⇒ x = 270
(3) Let the two articles be 7x and 4x rupees.
The cost of first article (7x) = Rs 2800
∴ 7x = 2800
⇒ x = 400
Therefore the cost of second article is (4 × 400) = Rs 1600.
(4) Let the length and width be 8x and 5x cm.
The width of the sheet (5x) = 17.5
∴ 5x = 17.5
⇒ x = 3.5
Therefore the length of the sheet = (8 × 3.5) cm = 28 cm.
(5) Let the age of A and B be 6x and 5x years respectively.
A’s age (6x) = 18 years
∴ 6x = 18
⇒ x = 3
Then, B’s age is = (5 × 3) = 15 years.
(7) 15cm : 2 m : : 10 sec : 3 min
Here, 2 m = (2 × 100) = 200cm and 3 min = (3 × 60) = 180 sec
= 15 cm : 200 cm : : 10sec : 180 sec
= 3 : 40 : : 1 : 18
No, they don’t from a proportion.
(8) 2 kg : 80 kg : : 25 g : 625 g
= 2 : 80: : 25 : 625
= 1 : 40 : : 1 : 25
No, they don’t from a proportion.
(9) 10 : 350 = x : 175
⇒ 350x = 1750
⇒ x = 1750/350
⇒ x = 5
(10) (i) Let the length of shorter rope be x m.
∴ 7 : 5 = 22.5 : x
⇒ 7x = 22.5 × 5
⇒ x = 112.5/7 = 16.07 m
(ii) Let the length of longer rope be x m.
∴ 7 : 5 = 9.8 × x
⇒ 7x = 9.8 × 5
⇒ x = 49/7 = 7 m
(11) 4 : x = x : 9
⇒ x2 = 36
⇒ x = √36 = 6
(12) 25 : 35 = 35 : x
⇒ 25x = 1225
⇒ x = 1225/25 = 49