7th Ratio and Proportion
1. The comparison of two quantities of the same kind by means of division is termed as ___.
2. The two quantities to be compared are called the ________ of the ratio.
3. The first term of the ratio is called the _________ and the second term is called the ___.
4. In a ratio, only two quantities of the __________ unit can be compared.
5. If the terms of the ratio have common factors, we can reduce it to its lowest terms by
cancelling the _____.
6. When both the terms of a ratio are multiplied or divided by the same number (other than
zero) the ratio remains _________ .The obtained ratios are called__________.
7. In a ratio the order of the terms is very important. (Say True or False)
8. Ratios are mere numbers. Hence units are not needed. (Say True or False)
9. Equality of two ratios is called a __________. If a,b;c,d are in proportion, then a:b::c:d .
10. In a proportion, the product of extremes =___________
Help Box:
1. Find 5 equivalent ratios of 2:7
2. Reduce 270 : 378 to its lowest term.
3. Find the ratio of 9 months to 1 year
4. If a class has 60 students and the ratio of boys to girls is 2:1, find the number of boys and
girls.
5. A ribbon is cut into 3 pieces in the ratio 3: 2: 7. If the total length of the ribbon is 24 m, find
the length of each piece.
6. The ratio of boys to girls in a class is 4 : 5. If the number of boys is 20, find the number of
girls.
7. If A : B = 4 : 6, B : C = 18 : 5, find the ratio of A : B : C.
8. A bronze statue is made of copper, tin and lead metals. It has1/10 of tin , 1/4of lead and
the rest copper. Find the part of copper in the bronze statue.
7th Direct variation and indirect variation
In direct variation, when a given quantity (x) is changed in some ratio then the other quantity(y) is also changed in the same ratio. Then x/ y = constant
In Indirect variation, when a given quantity (x) is changed in some ratio then the other quantity(y) is do not changed in the same ratio. Then xy = constant
Þ It can be stated that if two quantities vary inversely, their product is a constant
1. Choose the correct answer
i) If the cost of 8 kgs of rice is Rs 160, then the cost of 18 kgs of rice is
(A) Rs.480 (B) Rs 180 (C) Rs 360 (D) Rs 1280
ii) If the cost of 7 mangoes is `35, then the cost of 15 mangoes is
(A) Rs 75 (B) Rs 25 (C) Rs 35 (D) Rs 50
iii) A train covers a distance of 195 km in 3 hrs. At the same speed, the distance travelled in 5 hours is
v) If 18 men can do a work in 20 days, then 24 men can do this work in
(A) 20 days (B) 22 days (C) 21 days (D) 15 days
1. If x varies directly as y, complete the given tables:
2. If x varies inversely as y, complete the given tables:
3. A car travels 360 km in 4 hrs. Find the distance it covers in 6 hours 30 mins at the same speed
5. A book contains 120 pages. Each page has 35 lines . How many pages will the book
contain if every page has 24 lines per page?
6. A car travels 60 km in 45 minutes. At the same rate, how many kilo metres will it travel in
one hour?
7. A car takes 5 hours to cover a particular distance at a uniform speed of 60 km / hr. How
long will it take to cover the same distance at a uniform speed of 40 km / hr?
8. 150 men can finish a piece of work in 12 days. How many days will 120 men take to finish
the same work?
9. A troop has provisions for 276 soldiers for 20 days. How many soldiers leave the troop so
that the provisions may last for 46 days?
10. A book has 70 pages with 30 lines of printed matter on each page. If each page is to
have only 20 lines of printed matter, how many pages will the book have?
11. There are 800 soldiers in an army camp. There is enough provisions for them for 6o
days. If 400 more soldiers join the camp, for how many days will the provisions last?
12. A wheel makes 48 revolutions in 3 seconds. How many revolutions does it make in 30
seconds?
1) Write the following as a percent: (i) 20:100 (ii) 100:93(iii)100/100 (iv) 0.07
2) Write the following percent as a ratio: (i) 43% (ii) 17 ^{1}/_{2}(iii) 5% (iv) 33 ^{1}/_{3} %
3) Write the following percent as a fraction: (i) 25% (ii) 12 ^{1}/_{2}% 2 (iii) 33%
4) 9/10 of your blood is water. What % of your blood is not water.
5) 2/5 of your body weight is muscle. What % of body is muscle?
In a class of 35 students, 7 students were absent on a particular day. What percentages of
the students were absent?
5. Ram bought 36 mangoes. 5 mangoes were rotten. What percentage of the mangoes was
rotten?
6. In a class of 50, 23 were girls and the rest were boys. What is the percentage of girls and
the percentage of boys?
7. Ravi got 66 marks out of 75 in Mathematics and 72 out of 80 in Science. In which subject
did he score more?
8. Express as a decimal (a) 25.7% (b) 15%
9. Find the value of (a)% 1/2 of 200. (b) 0.75% of 40 kg.
10. In 2011, the population of a town is 1,50,000. If it is increased by 10% in the next year, find the population in 2012.
11. The percentage of literacy in a village is 47%. Find the number of illiterates in the village,
if the population is 7,500.
12. Is it true? 20% of 25 is same as 25% of 20.
13. The tax in a restaurant is 1.5% of your total bill.
a) Write the tax % as a decimal. b) A family of 6 members paid a bill of ` 750. What is the tax
for their bill amount? c) What is the total amount that they should pay at the restaurant?
14. 1) Any fraction with its denominator 100 is called __________
2)1/2 = % 3) 35% =  ( in fraction)
4) 0.05 = % 5)1/4 =  %
1. Choose the correct answer:
i) If the cost price of a bag is Rs. 575 and the selling price is Rs.625, then there is a profit of
Rs.
(A) 50 (B) 575 (C) 625 (D) none of these
ii) If the cost price of the box is Rs.155 and the selling price is Rs.140, then there is a loss of
Rs.
(A) 155 (B) 140 (C) 15 (D) none of these
iii) If the selling price of a bag is `235 and the cost price is `200, then there is a
(A) profit of Rs.235 (B) loss of Rs.3 (C) profit of Rs.35 (D) loss of Rs.200
iv) Gain or loss percent is always calculated on
(A) cost price (B) selling price (C) gain (D) loss
v) If a man makes a profit of Rs.25 on a purchase of Rs.250, then profit% is
(A) 25 (B) 10 (C) 250 (D) 225
1. Sanjay bought a bicycle for Rs. 5,000. He sold it for Rs.600 less after two years. Find the selling price and the loss percent.
2. A fruit seller bought 8 boxes of grapes at Rs.150 each. One box was damaged. He sold the remaining boxes at Rs.190 each. Find the profit / loss percent.
3. A shop keeper bought 10 bananas for `100. 2 bananas were rotten. He sold the remaining bananas at the rate of Rs. 11 per banana. Find his gain or loss % 6. A shop keeper purchased 100 ball pens for Rs. 250. He sold each pen for Rs. 4. Find the profit percent.
4. A vegetable vendor bought 40 kg of onions for Rs. 360. He sold 36 kg at Rs. 11 per
5. A trader mixes two kinds of oil, one costing Rs. 100 per Kg. and the other costing `80 per Kg. in the ratio 3: 2 and sells the mixture at Rs. 101.20 per Kg. find his profit or loss percent.
6. Sathish sold a camera to Rajesh at a profit of 10 %. Rajesh sold it to John at a loss of 12 %. If John paid Rs. 4,840, at what price did Sathish buy the camera?
7. The profit earned by a book seller by selling a book at a profit of 5% is Rs. 15 more than when he sells it at a loss of 5%. Find the Cost Price of the book.
2. Find the simple interest and the amount due on Rs. 7,500 at 8 % per annum for 1 year 6 months.
3. Find the simple interest and the amount due on Rs. 6,750 for 219 days at 10 % per annum.
4. Rahul borrowed Rs. 4,000 on 7th of June 2006 and returned it on 19th August2006. Find the amount he paid, if the interest is calculated at 5 % per annum
5. Find the rate percent per annum when a principal of Rs. 7,000 earns a S.I. of Rs.1, 680 in 16 months.
6. Vijay invested Rs.10, 000 at the rate of 5 % simple interest per annum. He received Rs.11, 000 after some years. Find the number of years.
7. A sum of money triples itself at 8 % per annum over a certain time. Find the number of years.
8. A certain sum of money amounts to Rs.10, 080 in 5 years at 8 %. Find the principal
9. A certain sum of money amounts to Rs. 8,880 in 6 years and Rs. 7,920 in 4 years
respectively. Find the principal and rate percent.
10. Find the principal that earns `250 as S.I. in 2^{1}/_{2 } years at 10 % per annum.
11. In how many years will a sum of Rs. 5,000 amount to Rs.5,800 at the rate of 8 % per
annum.
12. A sum of money doubles itself in 10 years. Find the rate of interest.
13. A sum of money doubles itself at 12^{1}/_{2} % per annum over a certain period of time. Find the number of years.
14. A certain sum of money amounts to Rs. 6,372 in 3 years at 6 % Find the principal.
15. A certain sum of money amounts to Rs. 6,500 in 3 years and Rs. 5,750 in 1^{1}/_{2 }years respectively. Find the principal and the rate percent?
16. Find the rate per cent at which, a sum of money becomes 9/4 times in 2 years.
17) If Ram needs Rs. 6, 00,000 after 10 years, how much should he invest now in a bank if the bank pays 20 % interest p.a?
Complete the following statements using the help box:
1. The comparison of two quantities of the same kind by means of division is termed as ___.
2. The two quantities to be compared are called the ________ of the ratio.
3. The first term of the ratio is called the _________ and the second term is called the ___.
4. In a ratio, only two quantities of the __________ unit can be compared.
5. If the terms of the ratio have common factors, we can reduce it to its lowest terms by
cancelling the _____.
6. When both the terms of a ratio are multiplied or divided by the same number (other than
zero) the ratio remains _________ .The obtained ratios are called__________.
7. In a ratio the order of the terms is very important. (Say True or False)
8. Ratios are mere numbers. Hence units are not needed. (Say True or False)
9. Equality of two ratios is called a __________. If a,b;c,d are in proportion, then a:b::c:d .
10. In a proportion, the product of extremes =___________
Help Box:
1) Ratio 2) terms 3) antecedent, consequent 4) same 5) common terms 6) unchanged, equivalent ratios 7) True 8) True 9) proportion 10) product of means
1. Find 5 equivalent ratios of 2:7
2. Reduce 270 : 378 to its lowest term.
3. Find the ratio of 9 months to 1 year
4. If a class has 60 students and the ratio of boys to girls is 2:1, find the number of boys and
girls.
5. A ribbon is cut into 3 pieces in the ratio 3: 2: 7. If the total length of the ribbon is 24 m, find
the length of each piece.
6. The ratio of boys to girls in a class is 4 : 5. If the number of boys is 20, find the number of
girls.
7. If A : B = 4 : 6, B : C = 18 : 5, find the ratio of A : B : C.
8. A bronze statue is made of copper, tin and lead metals. It has1/10 of tin , 1/4of lead and
the rest copper. Find the part of copper in the bronze statue.
7th Direct variation and indirect variation
In direct variation, when a given quantity (x) is changed in some ratio then the other quantity(y) is also changed in the same ratio. Then x/ y = constant
In Indirect variation, when a given quantity (x) is changed in some ratio then the other quantity(y) is do not changed in the same ratio. Then xy = constant
Þ It can be stated that if two quantities vary inversely, their product is a constant
1. Choose the correct answer
i) If the cost of 8 kgs of rice is Rs 160, then the cost of 18 kgs of rice is
(A) Rs.480 (B) Rs 180 (C) Rs 360 (D) Rs 1280
ii) If the cost of 7 mangoes is `35, then the cost of 15 mangoes is
(A) Rs 75 (B) Rs 25 (C) Rs 35 (D) Rs 50
iii) A train covers a distance of 195 km in 3 hrs. At the same speed, the distance travelled in 5 hours is
(A) 195 km. (B) 325 km. (C) 390 km. (D) 975 km.
iv) If 8 workers can complete a work in 24 days, then 24 workers can complete the same work in
(A) 8 days (B) 16 days (C) 12 days (D) 24 days
(A) 8 days (B) 16 days (C) 12 days (D) 24 days
v) If 18 men can do a work in 20 days, then 24 men can do this work in
(A) 20 days (B) 22 days (C) 21 days (D) 15 days
1. If x varies directly as y, complete the given tables:
x

1

1

9

15
 
y

2

10

16

2. If x varies inversely as y, complete the given tables:
x

20

10

40

50
 
y

50

250

3. A car travels 360 km in 4 hrs. Find the distance it covers in 6 hours 30 mins at the same speed
4. 7 men can complete a work in 52 days. In how many days will 13 men finish the same work?
5. A book contains 120 pages. Each page has 35 lines . How many pages will the book
contain if every page has 24 lines per page?
6. A car travels 60 km in 45 minutes. At the same rate, how many kilo metres will it travel in
one hour?
7. A car takes 5 hours to cover a particular distance at a uniform speed of 60 km / hr. How
long will it take to cover the same distance at a uniform speed of 40 km / hr?
8. 150 men can finish a piece of work in 12 days. How many days will 120 men take to finish
the same work?
9. A troop has provisions for 276 soldiers for 20 days. How many soldiers leave the troop so
that the provisions may last for 46 days?
10. A book has 70 pages with 30 lines of printed matter on each page. If each page is to
have only 20 lines of printed matter, how many pages will the book have?
11. There are 800 soldiers in an army camp. There is enough provisions for them for 6o
days. If 400 more soldiers join the camp, for how many days will the provisions last?
12. A wheel makes 48 revolutions in 3 seconds. How many revolutions does it make in 30
seconds?
7^{th} Percentage
The word ‘Percent’ is derived from the Latin word ‘Percentum’, which means ‘per hundred’ or ‘hundredth’ or ‘out of 100’.
• Percentage also means ‘percent’.
• Symbol used for percent is %
• Any ratio x : 100 is called ‘Percent’.
1) Write the following as a percent: (i) 20:100 (ii) 100:93(iii)100/100 (iv) 0.07
2) Write the following percent as a ratio: (i) 43% (ii) 17 ^{1}/_{2}(iii) 5% (iv) 33 ^{1}/_{3} %
3) Write the following percent as a fraction: (i) 25% (ii) 12 ^{1}/_{2}% 2 (iii) 33%
4) 9/10 of your blood is water. What % of your blood is not water.
5) 2/5 of your body weight is muscle. What % of body is muscle?
In a class of 35 students, 7 students were absent on a particular day. What percentages of
the students were absent?
5. Ram bought 36 mangoes. 5 mangoes were rotten. What percentage of the mangoes was
rotten?
6. In a class of 50, 23 were girls and the rest were boys. What is the percentage of girls and
the percentage of boys?
7. Ravi got 66 marks out of 75 in Mathematics and 72 out of 80 in Science. In which subject
did he score more?
8. Express as a decimal (a) 25.7% (b) 15%
9. Find the value of (a)% 1/2 of 200. (b) 0.75% of 40 kg.
10. In 2011, the population of a town is 1,50,000. If it is increased by 10% in the next year, find the population in 2012.
11. The percentage of literacy in a village is 47%. Find the number of illiterates in the village,
if the population is 7,500.
12. Is it true? 20% of 25 is same as 25% of 20.
13. The tax in a restaurant is 1.5% of your total bill.
a) Write the tax % as a decimal. b) A family of 6 members paid a bill of ` 750. What is the tax
for their bill amount? c) What is the total amount that they should pay at the restaurant?
14. 1) Any fraction with its denominator 100 is called __________
2)1/2 = % 3) 35% =  ( in fraction)
4) 0.05 = % 5)1/4 =  %
7^{th} Profit and Loss
The price at which any one buys goods at the market is called the Cost Price(C.P.).
The price at which one can sell the goods at the market is called the Selling Price (S.P.).
Additional amount given or taken for CP is called the profit.
1. Choose the correct answer:
i) If the cost price of a bag is Rs. 575 and the selling price is Rs.625, then there is a profit of
Rs.
(A) 50 (B) 575 (C) 625 (D) none of these
ii) If the cost price of the box is Rs.155 and the selling price is Rs.140, then there is a loss of
Rs.
(A) 155 (B) 140 (C) 15 (D) none of these
iii) If the selling price of a bag is `235 and the cost price is `200, then there is a
(A) profit of Rs.235 (B) loss of Rs.3 (C) profit of Rs.35 (D) loss of Rs.200
iv) Gain or loss percent is always calculated on
(A) cost price (B) selling price (C) gain (D) loss
v) If a man makes a profit of Rs.25 on a purchase of Rs.250, then profit% is
(A) 25 (B) 10 (C) 250 (D) 225
1. Sanjay bought a bicycle for Rs. 5,000. He sold it for Rs.600 less after two years. Find the selling price and the loss percent.
2. A fruit seller bought 8 boxes of grapes at Rs.150 each. One box was damaged. He sold the remaining boxes at Rs.190 each. Find the profit / loss percent.
3. A shop keeper bought 10 bananas for `100. 2 bananas were rotten. He sold the remaining bananas at the rate of Rs. 11 per banana. Find his gain or loss % 6. A shop keeper purchased 100 ball pens for Rs. 250. He sold each pen for Rs. 4. Find the profit percent.
4. A vegetable vendor bought 40 kg of onions for Rs. 360. He sold 36 kg at Rs. 11 per
kg. The rest were sold at Rs. 4.50 per kg as they were not very good. Find his profit / loss Percent.
5. A trader mixes two kinds of oil, one costing Rs. 100 per Kg. and the other costing `80 per Kg. in the ratio 3: 2 and sells the mixture at Rs. 101.20 per Kg. find his profit or loss percent.
6. Sathish sold a camera to Rajesh at a profit of 10 %. Rajesh sold it to John at a loss of 12 %. If John paid Rs. 4,840, at what price did Sathish buy the camera?
7. The profit earned by a book seller by selling a book at a profit of 5% is Rs. 15 more than when he sells it at a loss of 5%. Find the Cost Price of the book.
7^{th} Simple Interest
1. Radhika invested Rs.5,000 for 2 years at 11 % per annum. Find the simple interest and the amount received by him at the end of 2 years.
2. Find the simple interest and the amount due on Rs. 7,500 at 8 % per annum for 1 year 6 months.
3. Find the simple interest and the amount due on Rs. 6,750 for 219 days at 10 % per annum.
4. Rahul borrowed Rs. 4,000 on 7th of June 2006 and returned it on 19th August2006. Find the amount he paid, if the interest is calculated at 5 % per annum
5. Find the rate percent per annum when a principal of Rs. 7,000 earns a S.I. of Rs.1, 680 in 16 months.
6. Vijay invested Rs.10, 000 at the rate of 5 % simple interest per annum. He received Rs.11, 000 after some years. Find the number of years.
7. A sum of money triples itself at 8 % per annum over a certain time. Find the number of years.
8. A certain sum of money amounts to Rs.10, 080 in 5 years at 8 %. Find the principal
9. A certain sum of money amounts to Rs. 8,880 in 6 years and Rs. 7,920 in 4 years
respectively. Find the principal and rate percent.
10. Find the principal that earns `250 as S.I. in 2^{1}/_{2 } years at 10 % per annum.
11. In how many years will a sum of Rs. 5,000 amount to Rs.5,800 at the rate of 8 % per
annum.
12. A sum of money doubles itself in 10 years. Find the rate of interest.
13. A sum of money doubles itself at 12^{1}/_{2} % per annum over a certain period of time. Find the number of years.
14. A certain sum of money amounts to Rs. 6,372 in 3 years at 6 % Find the principal.
15. A certain sum of money amounts to Rs. 6,500 in 3 years and Rs. 5,750 in 1^{1}/_{2 }years respectively. Find the principal and the rate percent?
16. Find the rate per cent at which, a sum of money becomes 9/4 times in 2 years.
17) If Ram needs Rs. 6, 00,000 after 10 years, how much should he invest now in a bank if the bank pays 20 % interest p.a?
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