# Selina Concise Solutions for Chapter 6 Ratio and Proportion (including Sharing in Ratio) Class 7 ICSE Mathematics

**Exercise 6 (A)**

**1. Express each of the given ratio in its simplest form :(i) 22 : 66 (ii) 1.5 : 2.5 (iv) 40 kg : 1 quintal (v) 10 paise : ₹ 1 (vi) 200m : 5 km (vii) 3 hours : 1 day(viii) 6 months : 4/3 years **

**Answer **

**2. Divide 64 cm long string into two parts in the ratio 5 : 3 . **

**Answer **

Sum of ratios = 5+3 = 8

∴ first part = 5/8 of 64 cm = 40 cm

Second part = 3/8 of 64 cm = 24 cm

**3. Rs. 720 is divided between x and y in the ratio 4 : 5 . How many rupees will each get ? **

**Answer **

Total amount = Rs. 720 Ratio between x, y = 4 : 5

Sum of ratios = 4+ 5 = 9

x's share = 4/9 of Rs. 720 = Rs. 320

y's share = 5/9 of Rs. 720 = Rs. 400

**4. The angles of a triangle are in the ratio 3 : 2 : 7. Find each angle. **

**Answer **

Ratio in angles of a triangle = 3 : 2 : 7

Sum of ratios = 3 + 2 + 7 = 12

Sum of angles of a triangle = 180°

∴ First angle = 3/12 ×180°= 45°

Second angle = 2/12 ×180°= 30°

Third angle = 7/12 ×180°= 105°

**5. A rectangular field is 100 m by 80 m. Find the ratio of**

**(i) length to its breadth**

**(ii) breadth to its perimeter.**

**Answer**

**6. The sum of three numbers, whose ratios are is 4917.Find the**

**numbers.**

**Answer**

**7. The ratio between two quantities is 3 : the first is Rs. 810, find the second.**

**Answer**

Sum of ratio = 3+ 4 = 7

∴Second quantity = Rs. (810 × 4)/3

= Rs. 270 × 4 = Rs. 1080

**8. Two numbers are in the ratio 5 : 7. Their difference is 10. Find the numbers .**

**Answer**

**9. Two numbers are in the ratio 10 : 11. Their sum is 168. Find the numbers.**

**Answer**

**10. A line is divided in two parts in the ratio 2.5 : 1.3. If the smaller one is 35T cm, find**

**the length of the line.**

**Answer**

**11. In a class, the ratio of boys to the girls is 7:8. What part of the whole class are**

**girls.**

**Answer**

**12. The population of a town is ’ 50,000, out of which males are 1/3 of the whole**

**population. Find the number of females. Also, find the ratio of the number of**

**females to the whole population.**

**Answer**

**13. Ten gram of an alloy of metals A and B contains 7.5 gm of metal A and the rest is**

**metal B. Find the ratio between :**

**(i) the weights of metals A and B in the alloy.**

**(ii) the weight of metal B and the weight of the alloy.**

**Answer**

**(i)**Ratio between A and B = 7.5 : 2.5

= 75/10 : 25/10 = 3 : 1

**(ii)**Ratio between B and total alloy

= 2.5 : 10 = 25/10 : 10

= 25 : 100 = 1 : 4

**14. The ages of two boys A and B are 6 years 8 months and 7 years 4 months**

**respectively. Divide Rs. 3,150 in the ratio of their ages.**

**Answer**

**15. Three persons start a business and spend Rs. 25,000; Rs. 15,000 atid Rs. 40,000**

**respectively. Find the share of each out of a profit of Rs. 14,400 in a year.**

**Answer**

**16. A plot of land, 600 sq m in area, is divided between two persons such that the**

**first person gets three-fifth of what the second gets. Find the share of each.**

**Answer**

Let second's share = x

Then first share = 3x/5

∴ Ratio between them

3x/5 : x

⇒ 3/5 : 1 = 3 : 5

Sum of ratios = 3 + 5 = 8

∴ Share of first person = (600/8) × 3

= 225 sq. m

and second share = (600/8) × 5 = 375 sq.m

**17. Two poles of different heights are standing vertically on a horizontal field. At a**

**particular time, the ratio between the lengths of their shadows is 2 :3. If the height**

**of the smaller pole is 7.5 m, find the height of the other pole.**

**Answer**

∴ Height of smaller pole = 7.5 m

Height of taller pole = (7.5 × 3)/2

= 22.5/2 = 11.25 m

**18. Two numbers are in the ratio 4 : 7. If their L.C.M. is 168, find the numbers.**

**Answer**

**19. is divided between A and B in such a way that A gets half of B. Find :**

**(i) the ratio between the shares of A and B.**

**(ii) the share of A and the share of B.**

**Answer**

(i) A gets half of B

Hence, ratio between A and B = 1/2

= 1 : 2

(ii) Sum of ratios = 1 + 2 =3

∴ A' shares = (300 × 1)/3 = ₹ 100

∴ B' shares = (300 × 2)/3 = ₹ 200

**20. The ratio between two numbers is 5 : 9. Find the numbers, if their H.C.F. is 16.**

**Answer**

**21. A bag contains ₹ 1,600 in the form of ₹10 and ₹20 notes. If the ratio between the**

**numbers of ₹10 and ₹20 notes is 2 : 3; find the total number of notes in all.**

**Answer**

It contains notes in the denomination of ₹ 10 and 20

Ratio between the number of ₹10 and 20

notes is = 2 : 3

Let number of ₹10 note = x

and number of ₹20 notes = y

According to condition,

10x + 20y = 1600

**....(i)**

and x = 2y/3

**...(ii)**

Now, substitute the value of x in eq. (i)

∴ y = 60

Now, substitute the value of y in eq. (ii), we get

x = (2/3) × 60 = 40

Total number of notes in all = x + y

= 60 +40 = 100 notes

**22. The ratio between the prices of a scooter and a refrigerator is 4 : 1. If the scooter**

**costs ₹45,000 more than the refrigerator, find the price of the refrigerator.**

**Answer**

**Exercise 6 (B)**

**1. Check whether the following quantities form a proportion or not ?**

(i) 3x , 7x, 24 and 56

(ii) 0.8, 3, 2.4 and 9

(iv) 0.4, 0.5, 2.9 and 3.5

(i) 3x , 7x, 24 and 56

(ii) 0.8, 3, 2.4 and 9

(iv) 0.4, 0.5, 2.9 and 3.5

**Answer**

If these are in proportion, then

3x × 56 = 7x × 24

⇒ 168x = 168x

which is true.

Hence 3x, 7x, 24 and 56 are in proportion.

if 0.8 × 9 = 3× 2.4

⇒ 7.2 = 7.2

which is true

Hence 0.8, 3, 2.4 and 9 are in proportion.

if 0.4 × 3.5 = 0.5 × 2.9

⇒ 1.40 = 1.45

which is not true

Hence, 0.4, 0.5, 2.9 and 3.5 are not in proportion.

**2. Find the fourth proportional of**

(i) 3, 12 and 4

(ii) 5, 9 and 45

(iii) 2.1, 1.5 and 8.4

(iv) 1/3, 2/5 and 8.4

(v) 4 hours 40 minutes, 1 hour 10 minutes and 16 hours.

(i) 3, 12 and 4

(ii) 5, 9 and 45

(iii) 2.1, 1.5 and 8.4

(iv) 1/3, 2/5 and 8.4

(v) 4 hours 40 minutes, 1 hour 10 minutes and 16 hours.

**Answer**

= (12×4)/3

= (9×45)/5

= (1.5×8.4)/2.1

1 hours 10 minutes and 16 hours

4 hours 40 minutes = 4 × 60 + 40

= 240 + 40 = 280

1 hour 10 minutes = 1 × 60 + 10

= 60 + 10 = 70 minutes

16 hours = 16 × 60 = 960 minutes

∴ Fourth proportional = (70 × 960)/280

= 240 minutes = 240/60 = 4 hours

**3. Find the third proportional of**

(i) 27 and 8

(ii) 2 m 40cm and 40 cm

(iii) 1.8 and 0.6

(iv) 1/7 and 3/14

(v) 1.6 and 0.8

(i) 27 and 8

(ii) 2 m 40cm and 40 cm

(iii) 1.8 and 0.6

(iv) 1/7 and 3/14

(v) 1.6 and 0.8

**Answer**

= (9 × 9)/27

or 240 cm and 40cm

= (40×40)/240

= (0.6×0.6)/1.8

= 1/5

**4. Find the mean proportional between**

(i) 16 and 4

(ii) 3 and 27

(iii) 0.9 and 2.5

(iv) 0.6 and 9.6

(v) 1/4 and 1/16

(i) 16 and 4

(ii) 3 and 27

(iii) 0.9 and 2.5

(iv) 0.6 and 9.6

(v) 1/4 and 1/16

**Answer**

**5. (i) If A : B = 3 : 5 and B : C = 5 : 7, find A : B : C**

(ii) If x : y = 2 : 3 and y : z = 5 : 7, find x : y : z

(iii) If m : n = 4: 9 and n : s = 3 : 7, find m : s

(iv) If P : Q = 1/2 : 1/3 and find P : R.

(v) If a: b = 1.5 : 3.5 and b : c= 5 : 6, find a : c.

Find P : r

(ii) If x : y = 2 : 3 and y : z = 5 : 7, find x : y : z

(iii) If m : n = 4: 9 and n : s = 3 : 7, find m : s

(iv) If P : Q = 1/2 : 1/3 and find P : R.

(v) If a: b = 1.5 : 3.5 and b : c= 5 : 6, find a : c.

Find P : r

**Answer**

**6. If x : y = 5 : 4 and 2 : x = 3 : 8, find the value of y.**

**Answer**

**7. Find the value of x, when 2.5 : 4 = x : 7.5.**

**Answer**

4×x = 2.5 × 7.5

**8. Show that 2, 12 and 72 are in continued proportion.**

**Answer**

proportion if, a : b ∷ b : c

The numbers are 2, 12 and 72