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SChand Composite Mathematics Class 7 Chapter 8 Ratio , Proportion , Unitary Method Exercise 8C

Exercise 8 C

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Question 1

100gm of butter make 14 cakes . How many cakes 150 gm make ?

Sol :

100gm of butter make= 14 cakes

1 gm------------= $\frac{14}{100}$

150 gm ---------------------= $\frac{14}{100} \times 150=21$ cakes

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Question 2

A plane flies 405 km on 90 liter of fuel .

(i) How much fuel is needed for 540km ?

(ii) How far can it go is 50 liters ?

Sol :

Plane files 405 km on = 90 liters

---------1 km ------- = $\frac{90}{405}$

-------540 km ------= $\frac{90}{405} \times 540$

=120 liters

(ii) In 90 liters it can fly = 405 km

-------1 liter --------- = $\frac{405}{90}$

-------50 liters ------= $\frac{405}{90} \times 50$

= 225km

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Question 3

16 articles cost Rs 72 . What will be the cost of 30 articles ? How many articles can be bought for Rs 207 ?

Sol :

16 articles cost = Rs 72

1 article cost = $\frac{72}{16}$

30 article cost=$\frac{72}{16} \times 30$ = Rs 135

(ii) In Rs 72 articles bought = 16

---Rs 1 ------------ = $\frac{16}{72}$

----Rs 207 ---------= $\frac{16}{72} \times 207$

= 46 articles

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Question 4

A Journey of 552 km takes 6 days. How long will a journey o f 1012 km take. If it is done at the same rate?

Sol :

A journey of 552 km takes = 6 days

-----------1km ------- = $\frac{6}{552}$

--------------1012 km ---------= $\frac{6}{552} \times 1012$

=11 days

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Question 5

Two and a half liters of paint is used to cover 725 sq m of area .

(i) How much will be required to paint 2001 sqm of area ?

(ii) How much area in sq m can be covered by 4.75 liters of paint?

Sol:

To cover 725 sq m area paint used = 2.5L

------------1 sq m --------= $\frac{2.5}{725}$

------------- 2001 sq m ---------=$\frac{25}{725} \times 2001$

= 6.9 L

(ii) 2.5 L point covers = 725sqm

1L --------------------= $\frac{725}{2.5}$

4.75 ---------------=$\frac{725}{25} \times \frac{4.75}{100} \times 10$

= 1377.5 sqm

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Question 6

$5 \frac{1}{4} m^{3}$ of copper sheet weight 1563kg. What will be weight of $3 \frac{1}{2} \mathrm{~m}^{3}$ of sheet ?

Sol :

$\frac{21}{4}$ $m^{3}$ weight = 1563

1 $m^{3}$ -------------= $\frac{1563}{\frac{21}{4}}$

$\frac{7}{2} \mathrm{~m}^{3}$ weight = $1563 \times \frac{4}{21} \times \frac{7}{2}$

= 1042 kg Answer

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Question 7

Harsh takes 150 steps in walking a distance of 125 meters .

(i) What distance would be cover in 360 steps?

(ii) How many steps would be needed to cover a distance of 120 m ?

Sol :

(i) Harsh takes 150 steps covers distance = 125 m

-----------------1 step ------------- = $\frac{125}{150}$

------------360 steps-------------= $\frac{125}{150} \times 360$

=300 m

(ii) 125 m distance covered in = 150 steps

1m ---------- = $\frac{150}{125}$

120m -----------------= $\frac{150}{125} \times 120$= 144 steps

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Question 8

Fifteen chairs can be bought for Rs 3532.50 . How many chairs can be bought for Rs 5416.50 ?

Sol :

15 chairs can be bought for Rs 3532.50

Cost of Rs 3532.50 is = 15 chairs

---------Rs 1 ----------= $\frac{15}{3532.50}$

Chairs bought for = Rs 5416.50 = $\frac{15}{3532.50} \times 5416.50 .$

= 23 chairs Answer

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Question 9

45 packets of butter each weighing 100gm cost Rs 607.50 What be the cost of 18 packets of butter each weighing 500 gm ?

Sol :

If each packet weighting 100

Weight of 45 packets = $45 \times 100=4500 \mathrm{gm}$

Weight 18 packets of each weight = $18 \times 500$

$9000 \mathrm{gm}$

$4500 \mathrm{gm} \text { butter cost }=Rs 607.50$

1gm-----------$=\frac{607.50}{4500}$

9000gm ------------ =$\frac{607.50}{4500} \times 9000$

= Rs 1215 answer

SChand Composite Mathematics Class 7 Chapter 8 Ratio , Proportion , Unitary Method Exercise 8B

Exercise 8 B

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Question 1

Determine whether the following number are in proportion or not:

(i) $\frac{1}{2}, \frac{1}{4}, \frac{1}{7}, \frac{1}{14}$

Sol: Product of Extreme =$\frac{1}{2} \times \frac{1}{14}=\frac{1}{28}$

Product of means = $\frac{1}{4} \times \frac{1}{7}=\frac{1}{28}$

∵ Product of Extreme= Product of means

$\frac{1}{28}=\frac{1}{28}$

$\therefore \frac{1}{2},\frac{1}{4},\frac{1}{7},\frac{1}{14}$ are proportion

$\therefore \quad 12,15,4,5$ are in proportion

(ii) $12,15,4,5$

Sol: $12 \times 5=60$

$15 \times 4=60$

60=60

(iii) $2,3 \frac{1}{2}, 3,4 \frac{1}{2}$ = $2, \frac{7}{2}, 3, \frac{9}{2}$

Sol: $2 \times \frac{9}{2}=9$ ; $\frac{7}{2} \times 3=\frac{21}{2}$

∵ Product of extreme≠ Product of means

$2,3 \frac{1}{2}, 3,4 \frac{1}{2}$ are not in proportions

(iv) $1.2,1.6,0.9,1.2$

Sol: $1.2 \times 1.2=1.44$ ; $1.6 \times 0.9=1.44$

∵ Product of extreme = product of means

1.44= 1.44

∵ $1.2,1.6,0.9,1.2$ are in Proportion

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Question 2

Find the value of x in each of the given proportions:

(i) 0.9: 0.6:: x : 3

Sol: $0.6 \times x=0.9 \times 3$

$x=\frac{0.9 \times 3}{0.6}=4.5$

(ii) $x: 5:: 28: 35$

Sol: $x \times 35=5 \times 28$

=x = $\frac{5 \times 28}{35}$

= x=4

(iii) $1.6: x:: 0.12: 0.24$

Sol: $x \times 0.12=1.6 \times 0.24$

$\Rightarrow \quad x=\frac{1.6 \times 0.24}{0.12}$

=x = 3.2

(iv) $\frac{1}{15}: \frac{1}{4}:: x: \frac{1}{5}$

Sol: $\frac{1}{4} \times x=\frac{1}{15} \times \frac{1}{5}$

$\Rightarrow x=\frac{4}{75}$

(v) $16: x: x: 25$

Sol: $\Rightarrow x \times x=16 \times 25$

$\Rightarrow x^{2}=16 \times 25$

$\Rightarrow x=4 \times 5$

$\Rightarrow x=20$

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Question 3

Find the fourth proportional to :

(i) $8, 32,17, x$

Sol: $8 \times x=32 \times 17$

$x=\frac{32 \times 17}{8}$

x = 68

(ii) $8.1,1.2,2.7,x$

Sol:

$8.1 \times x=1.2 \times 2.7$

x = $\frac{1.2 \times 2.7}{8.1}$

x= 0.4

(iii) $\frac{1}{3}, \frac{1}{5}, \frac{1}{7}, x$

Sol: $\frac{1}{3} \times x=\frac{1}{5} \times \frac{1}{7}$

$x=\frac{3}{35}$ Ans

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Question 4

Find the mean proportional between

(i) 144 and 225

Sol: Let x be the mean proportional between 144 and 225

Then $x^{2}=144 \times 225$

$x=\sqrt{144 \times 225}$

$x=12 \times 15$

$x=180$

(ii) 0.32 and 0.08

Sol: Let x be the mean proportional between 0.32 and 0.08

Then , $x^{2}=0.32 \times 0.08$

$x^{2}=0.0256$

$x^{2}=\frac{256}{10000} \Rightarrow x=\sqrt{\frac{256}{10000}}$

$x=\frac{16}{100}$

$\Rightarrow \quad x=0.16$

(iii) $\frac{1}{36}$ and $\frac{1}{9}$

Let $x$, Then $x^{2}=\frac{1}{36} \times \frac{1}{9}$

$x=\sqrt{\frac{1}{36} \times \frac{1}{9}}$

$x=\frac{1}{6} \times \frac{1}{3}$

$x=\frac{1}{18}$

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Question 5

Find the third proportional to:

(i) 32; 16

Sol: Let the third proportional to 32 and 16 be x

= 32, 16 , 16 ,x

= $32 \times x=16 \times 16 \Rightarrow x=\frac{16 \times 16}{32}$

=x =8 Answer

(ii) $4 \frac{1}{6}, 5$

Sol: $\frac{25}{6}, 5,5,x$

= $\frac{25}{6} \times 4=5 \times 5$

$\Rightarrow \quad x=25 \times \frac{6}{25}$

= x =6 answer

(iii) 4.2 , 0.7

Sol: 4.2 , 0.7 , 0.7 ,x

$4.2 \times x=0.7 \times 0.7$

x =$\frac{7}{60}$

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Question 6

Show that 6, 36 , 216 are in continued proportion

Sol :

6, 36, x ,216

= $36 \times 21=6 \times 216$

$x=\frac{6 \times 216}{36}$

x= 36

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Question 7

If 25 persons can dig a trench 36 m long in one day . Then find the number of persons required to dig a trench 108m long in one day.

Sol :

$25: 36:: x: 108$

$36 \times x=108 \times 25$

x= $\frac{108 \times 25}{36}$

x= 75

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Question 8

The label on a flavoured milk bottle states that there is 1.5 g of fat in 200ml. If you drink 500ml of that milk , how much fat would you be getting ?

Sol :

$1.5: 200:: x: 500$

= $200 \times x=1.5 \times 500$

x=$\frac{1.5 \times 500}{200}$

=3.75g

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Question 9

Rajat can type 3200 words in one hour . How many wards can be type in 15 minutes?

Sol :

3200: 60:: x :15

=$60 \times x=3200 \times 15$

x = $\frac{3200 \times 15}{60}$

x = 800 words

SChand Composite Mathematics Class 7 Chapter 8 Ratio , Proportion , Unitary Method Exercise 8A

Exercise 8 A

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Question 1

Express each of the following ratios in the simplest form:

(i) $28: 63$

Sol: $\frac{28}{63}$

= 4: 9

(ii) 105: 133

Sol: $\frac{105}{133}$

= 15: 19

(iii) 0.4: 0.6 66

Sol: $\frac{0 \cdot 4}{0 \cdot 6}$

= 2: 366

(iv) $2.7: 9$

Sol: $\frac{27}{90}$

=3:10

(v) $\frac{1}{4}: \frac{1}{9}$

Sol: $\frac{1}{4} \div \frac{1}{9}$

= $\frac{1}{4} \times \frac{9}{1} \quad \Rightarrow 9: 4$

(vi) $3 \frac{1}{2}: 2 \frac{1}{4}$

Sol: $\frac{7}{2} \div \frac{9}{4}$

= $\frac{7}{2} \times \frac{4}{9}$

= 14: 9

(vii) $\frac{1}{4}: \frac{1}{8}: \frac{1}{10}$

Sol: L.C.M of 4, 8 , 10 is = 40

$\frac{1}{4} \times 40: \frac{1}{8} \times 40: \frac{1}{10} \times 40=10: 5: 4$

(viii) $1 \frac{3}{4}: 2 \frac{2}{3}: 1 \frac{5}{6}$

Sol: $\frac{7}{4}: \frac{8}{3}: \frac{11}{6}$

(xi) $125 \mathrm{~g}: 1 \mathrm{~kg}$

Sol: $\frac{125}{1000}$

=1: 8

(x) 4 days : 2 weeks

4 days: 14 days

Sol: $\frac{4}{14}$

= 2: 7

(xi) 36 minutes to $1 \frac{1}{2}$ Hours

Sol: 36 mint to 90 Min

(xii) 76 ml

Sol: 1L 710ML

= 76 ml : 1710ML

$\Rightarrow \frac{76}{1710}$

= 2: 45

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Question 2

There are 2500 students in a school out of them 1100 are girls and the rest are boys , find the ratio of:

Sol: No of girls= 1100

No of boys = 2500- 1100= 1400

(i) Number of boys to number of girls

1400 : 1100 = 14: 11

(ii) Number of girls to number of students

1100: 2500 = 11: 25

(iii) Number of students to number of boys

2500: 1400= 25:14

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Question 3

The given figure shows a small garden. The shaded area is reserved for planting flowers and the rest of the area is for grass. Find the ratio of the area of the garden reserved for planting flowers to the area reserved for grass.

Sol: Area for flowers = $8 \times 3=24 \mathrm{~m}^{2}$

Area for grass = Total area - area of flowers

$\Rightarrow 12 \times 5-24$

$\Rightarrow \quad 60-24=36 \mathrm{~m}^{2}$

Area of flower : Area of for grass

$24: 36 \Rightarrow \frac{24}{36}=2: 3$

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Question 4

If the ratio of the length to the breadth of a rectangle be 5: 3 and its perimeter is 144m, find the length of the rectangle .

Sol: Let the length = 5x & Breadth = 3x

Perimeter of rectangle = $2 \times(l+b)$

$2 \times(5 x+3 x)=144$

$2 \times 8 x=144 \Rightarrow x=\frac{144}{16}=x=9$

Length= 5x = $5 \times 9=45 \mathrm{~m}$ Ans

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Question 5

Divide Rs 7400 among three people A, B , C in the ratio 3 : 5: 12

Sol: Let the amount = 3x : 5x : 12x

3x+5x+12x=7400

20x =7400

x $=\frac{7400}{20}$

x=370

A' s Amount =$3 \times 370=1100$

B's Amount =$5 \times 370=1850$

C's Amount = $12 \times 370=4440$

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Question 6

Divide 104 pencils among three children in the Ratio $\frac{1}{2}: \frac{1}{3}: \frac{1}{4}$

Sol :

L.C.M of 2,3,4 = 12

Simplified Ratio= $12 \times \frac{1}{2}: 12 \times \frac{1}{3}: 12 \times \frac{1}{4}$

$=6: 4: 3$

Let Sum = $6 x+4 x+3 x=104$

$\Rightarrow \quad 13 x=104$

$\Rightarrow \quad x=\frac{104}{13}$

x= 8

1st share = $6 \times 8=48$ pencils

2nd share = $4 \times 8=32$ pencils

3rd share = $3 \times 8=24$ pencils.

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Question 7

The angles of a quadrilateral are in the ratio 1: 2: 3 : 4 . If the sum of the angles of 9 quadrilateral is 360'. Find the measure of each angle.

Sol: Let angles = 1x : 2x : 3x : 4x

1x + 2x+3x + 4x = $360^{\circ} \Rightarrow 10 x=360^{\circ}$

x = $36^{\circ}$

First angle = $1 \times 36=36^{\circ}$

Second angle = $2 \times 36=72^{\circ}$

3rd angle = $3 \times 36=108^{\circ}$

4th angle = $4 \times 36=144^{\circ}$

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Question 8

If a: b = 5: 7 and b: c = 14: 15, find a: c

Sol: $\frac{a}{b}=\frac{5}{7} \quad ; \frac{b}{c}=\frac{14}{15}$

$\frac{a}{b} \times \frac{b}{c}=\frac{5}{7} \times \frac{14}{15}$

= $a: c=2: 3$

(ii) If x: y = 2: 7 and y: z = 9: 11 find x: y : z

Sol: $\frac{x}{y}=\frac{2}{7}$ , $\frac{y}{z}=\frac{9}{11}$

L.C.M = 7,9 is 64 : To find x: y: z we have to make y equal

$\frac{x}{y}=\frac{2 \times 9}{7 \times 9}=\frac{18}{63} ; \quad \frac{y}{2}=\frac{9}{11 \times 7} \times \frac{7}{7}=\frac{63}{77}$

$x: y=18: 63 ; \quad y: z=63: 77$

$x: y: z=18: 63: 77$

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Question 9

If l: m= $1 \frac{1}{2}: 1 \frac{3}{4}$ and m: n $2 \frac{1}{3}: 4 \frac{1}{5}$

Sol:

l: m =$\frac{3}{2}: \frac{7}{4}$= $\frac{3}{2} \div \frac{7}{4}$

=$\frac{3}{2} \times \frac{4}{7}$

$\frac{6}{7}=\frac{l}{m}$

m: n =$\frac{7}{3}: \frac{21}{5}$

$\frac{7}{3} \div \frac{21}{5}=$ $\frac{7}{3} \times \frac{5}{21}$

= $\frac{5}{9}=\frac{m}{n}$

=$\frac{1}{m}=\frac{6}{7}$

=$\frac{m}{n}=\frac{5}{9}$

(i) $\frac{l}{m} \times \frac{m}{n}$

= $\frac{6}{7} \times \frac{5}{9}$

=10:21= l: n Answer

(ii) l: m: n

Sol:

$\frac{1}{m}=\frac{6}{7}$

$\frac{m}{n}=\frac{5}{9}$

$\frac{l}{n}=\frac{10}{21}$

$\frac{1}{m} \times \frac{m}{n} =\frac{l}{n}$

Taking L.C.M of 7 and 5 =35

$\frac{1}{m}=\frac{6}{7} \times \frac{5}{5}=\frac{30}{35}$

$\frac{m}{n}=\frac{5}{9} \times \frac{7}{7}=\frac{35}{63}$

$\frac{1}{m} \times \frac{m}{n} =\frac{l}{n}$

$\frac{30}{35} \times \frac{35}{63} =\frac{30}{63}$

l : m : n = 30 : 35 : 63

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Question 10

Divide Rs 1545 between three people A, B and C such that A gets three fifths of what B gets and the ratio of the share of B to C is 6: 11

Sol :

Let the common factor be x

∴B=6x , C=11x

$A=\frac{3}{5} of B$

$A=\frac{3}{5} \times 6x$

$A=\frac{18x}{5}$

A+B+C=1545

$\frac{18x}{5}+\frac{6x}{1}+\frac{11x}{1}=1545$

$18x \times 1+6x \times 5 + 11x \times 5=1545 \times 5$

$18x+30x+55x=1545 \times 5$

103x=1545×5

$x=\frac{1545 \times 5}{103}$

x=75

B' share = $6 \times 75=450$

C' share = $11 \times 75=825$

A' share = $\frac{18}{5} \times x=\frac{18}{5} \times 75=270$

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Question 11

The ratio of the expenditure to the saving of a family is 7 : 3. Find income if the expenditure is Rs 6300.

Sol: Let Exp. saving= 7x: 3x

Income = Exp. + saving

$=7 x+3 x=10 x$

Given exp = 6300

7x = 6300 = $x=\frac{6300}{7} \Rightarrow 21=900$

Income = 10x = $10 \times 900=9000$ Answer

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Question 12

The ratio between the present age of p and Q is 3: 4 respectively . If Q'S Present age is 20

Year what will be the ratio of the ages after 5 years?

Sol: Let ratio of P and Q = 3x: 4x

Q's present age 4x = $20 \Rightarrow 21=\frac{20}{4}=5$

P 's Present age = $3x=3 \times 5=15$

After 5 years p's age = $15+5=20$ yr

Q's age = 20+5 = 25 yr

Ratio P: Q = 20 : 25= 4: 5 answer

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Question 13

Rina lost her weight in the ratio 5: 3 . Her original weight was 80 kg . what is her new weight ?

Sol: Original weight = $5 x=80 \Rightarrow x=\frac{80}{5}$

x= 16

New weight = 3x = $3 \times 16=48$kg

SChand Composite Mathematics Class 7 Chapter 8 Ratio , Proportion , Unitary Method Exercise 8C

Exercise 8 C

SChand Composite Mathematics Class 7 Chapter 8 Ratio , Proportion , Unitary Method Exercise 8B

Exercise 8 B

SChand Composite Mathematics Class 7 Chapter 8 Ratio , Proportion , Unitary Method Exercise 8A

Exercise 8 A

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