Problem and Solution: Part 5 (Ratio Exercise problem and solution, Proportion Exercise problem and solution, Rate & Partnership Exercise problem and solution)

Question: 27 Coffee A normally costs $ 100 per 1b. It is mixed with coffee B, which normally cost $ 70 per 1b, to form a mixture that costs $ 88 per 1b. If there are 10 1bs of the mix, how many pounds of coffee A is used in the mixture?
Option: (a) 4 (b) 5 (c) 6 (d) 7 (e) None

Explore: Let, a be the amount of coffee A present in per 1b of the mixture.
:. a x 100 + (1 - a)70 = 88
:. (100 - 70)a + 70 = 88
:. 30a = 18
:. a = 18/30 = 0.6 1b
:. In 10 1b, we have 6 1b of coffee A
Answer: (c)

Question: 28 Two blends of tea costing $ 2.80 and $ 3.20 per kg, respectively, are mixed in the proportion 2:3. The mixture is sold at $ 4.80 per kg, What is the percentage of profit?
Option: (a) 50.7 (b) 50.9 (c) 57.9 (d) 60

Explore: Let, tea of 1st kind and 2nd kind are mixed 2 kg & 3 kg, respectively. :. Total cost of 5 kg mixtrue = 2.8 x 2 + 3.2 x 3 = 5.6 + 9.6 =$ 15.2 Selling price of 5 kg = $ 4.8 x 5 = $ 24.0 :. Profit = $ 24 - $ 15.2 = $ 8.8 :. Percentage of profit = {(Profit)/(Original cost)} x 100% = {(8.8)/(15.2)} x 100% = 57.9 % Answer: (c)

Question: 29 Mr. John won an election where the ratio of his votes and those of his opponent, Mr. yunus was 4:3. The total number of voters was 581, of which 91 did not vote. Calculate the margin of votes by which Mr, Yunus was defeated.

Explore: No. of voters who applied their votes = 581 - 91 = 490
Ratio of votes of Mr. John  & Mr. Yunus = 4:3
Sum of the ratio = 4 + 3 = 7
:. Mr. John got = 490 x (4/7) = 280
Mr. Yunus got = 490 x (3/7) = 210
:. Margin of votes = 280 - 210 = 70
Answer: The margin of votes by which Mr, Yunus was defeated was 70.

Question: 30 A sum of money is distributed among A, B & C. The amount of money received by A & B were in the ratio 1:2. The amount of money received by B & C were in the ratio 3:4. How much money did A receive?
Option: (a) 989 (b) 999 (c) 968 (d) 990 (e) None

Explore: 5 + 7 + 10 = 22. So, the number must he divisible by 22, 968 & 990 are both divisible by 22. But since we are looking for the largest value, 990 is the answer.
Answer: (d)

Question: 31 $1105 was divided between A, B & C. The amount of money received by A & B were in the ratio 1:2. The amount of money received by B & C were in the ratio 3:4. How much money did A receive?
Option: (a) $ 205 (b) $ 195 (c) $ 1500 (d) $ 100 (e) None of these

Explore: A:B = 1:2 = 3:6
B:C = 3:4 = 6:8
:. A:B:C = 3:6:8
:. A got {(3)/(3+6+8)} x 1105 = (3/17) x 1105 = $ 195
Answer: (b)
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Ratio word problem exercise example 1 · Ratio word problem ...Ratio Worksheets | Ratio Worksheets for Teachers - Math Aidswww.math-aids.com/Ratios/?These Ratio Worksheets are perfect for teachers, homeschoolers, moms, dads, and children looking for some practice in Ratio problems.Ratios and Rates Word ... - ?Equivalent Ratio Worksheets - ?Simple Ratio WorksheetsRatios - Maths Tutorww.mathtutor.ac .uk/arithmetic/ratios/exercise?Ratios: Exercises. 1/6. 1. Attempt the following questions. Express the following ratios in their simplest form: 1. 2 to 10. 80 to 20. to 1. 3. 50p : £3.50. 6m : 30cm.Ratios, Proportions - Purplemathwww.purplemath.com/modules/ratio.htm?Explains the basic terminology and formatting of ratios, and demonstrates how to solve typical exercises. ... Return to the Purplemath home page.[PDF]Ratios - Mathcentrewww.mathcentre.ac.uk/resources/uploaded/mc-ty-ratios-2009-1.pdf?xercises so that they become second nature. ... www.mathcentre.ac.uk. 1 ... Exercises. 1. Express these ratios in their simplest form: (a) 2 to 10. (b) 80 to 20 (c) 1.Math Exerciseswww.emathematics.net/?Revise your understanding of proportional reasoning in maths. Here you will find exercises on ratios and proportions, direct proportions, inverse proportions, ...Ratios and Proportions Exercises - Mathematics - About.commath.about.com/od/Ratios-Proportions-Exercises/?Exercises for Ratios and Proportions. Exercises involving Ratios and Proportions. Proportions Word Problems Worksheet 2. A proportion is a set of 2 fractions ...Ratios and Proportions Math Worksheets! - edHelper.comedhelper.com/ratios.htm?Proportions: State whether the ratios are proportional (fractions) · Proportions: State whether the ratios are proportional (mixed ways of writing ratios)BBC - GCSE Bitesize: Ratioswww.bbc.co.uk › Home › Maths › Number?A secondary school revision resource for GCSE Maths about foundation level fractions, decimals and ratios.Searches related to ratio exercises mathhow to get ratiosmaths ratio and proportion exercisesratio worksheetsequivalent ratios worksheetratio and proportion worksheetratio problems worksheetratio sheetssimple ratio worksheetsRatios and Proportions Exercises - Mathematics - About.commath.about.com/od/Ratios-Proportions-Exercises/?Exercises for Ratios and Proportions. Exercises involving Ratios and Proportions. Proportions Word Problems Worksheet 2. 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Problem and Solution: Part 4 (Ratio Exercise problem and solution, Proportion Exercise problem and solution, Rate & Partnership Exercise problem and solution)

Question: 22 The ratio of gold and silver in an ornament weighing 42 gm is 4:3. How much gold will need to be added for the ratio of gold and silver to be 5:3?
Explore: The ratio of gold & silver = 4:3
Sum of the ratio = 4+3 = 7
The amount of gold = 42 gm x 4/7 = 24 gm
The amount of silver = 42 gm x 3/7 = 18 gm
Let, X gm gold will need to be added.
According to the question,
(24 +X ): 18 = 5:3
=> (24+X)/18 = 5/3
=> 72 + 3X = 90
=> 3X = 90 - 72 = 18
=> X = 18/3 = 6
Answer: 6 gm gold will need to be added

Question: 23 The ratio of boys and girls in a class is 1:2 and the classroom has 24 students. How many boys would have to be admitted to make ratio of boys to girls 1:1?

Option: (a) 6 (b) 8 (c) 10 (d) 12 (e) 14 Explore: Total no. of students = 24 Boys: Girls = 1:2 Sum of the ratio = 1+2 = 3 No. of boys = 24 x 1/3 = 8 No. of girls = 24 x 2/3 = 16 Let, X boys have to be admitted. According to the question, (8+X): 16 = 1:1 => (8+X) / 16 = 1/1 =1 => 8+X = 16 => X = 16 - 8 => X = 8 Answer: (b)

Question: 24 A jar contains white, red & green marbles in the ratio 2:3:4. Five more green marbles are added to make the ratio 2:3:5. How many white marbles are there in the jar?
Option: (a) 4 (b) 6 (c) 8 (d) 10 (e) None

Explore: Initially, white: green = 2:4
Let, G be the number of green marbles.
So, (White)/(Green) = 2/4 => (White)/G = 2/4
:. White = G/2
So, after 5 green marbles are added,
(White)/(Green) = (G/2)/(G + 5)
According to the problem,
(G/2)/(G + 5)
According to the problem,
(G/2)/(G + 5) = 2/5
=> (G)/(G+5) = 4/5 => 5G = 4G + 20
=> G = 20
:. No. of white marbles = 10
Answer: (d)

Question: 25 In an MBA class the ratio of number of commerce graduates to the number of science graduates is 2 to 5. If 2 more commerce graduates enter the class the ratio become 1 to 2. How many commerce graduates are in the class?

Explore: Let, there are 2X commerce graduates in the class and 5X science graduates.
According to the question,
(2X +2): 5X = 1:2
=> (2X+2)/5X = 1/2
=> 4X + 4 = 5X
=> 5X - 4X = 4
=> X = 4
Answer: No. of commerce graduates is 2 x 4 = 8

Question: 26 2 partners X & Y have 60% & 40% shares in business. After sometime a 3rd partner Z joined the business by investing $ 5 Lack & thus having 20% of the share in the business. What is Y's share now in the business?
Option: (a) 32% (b) 48% (c) 36% (d) 50% (e) None

Explore: Let, $X,Y,Z be X's, Y's & Z's share.
:. X/Y = 60/40 = 3/2
:. X = Y(3/2)
After Z joined the business we have
(X+Y)/Z = 80/20 [Z holds 20%, X & Y 80%]
:. ((5/2)Y)/500000 = 4 => (5/2)Y = 20,00,000
:. Y = 8,00,000
:. X = (3/2)Y = (3/2) x 8,00,000 = 12,00,000
:. X:Y:Z = 12,00,000 : 8,00,000 : 5,00,000
= 12 : 8 : 5
:. Y's share = 8/(12+8+5) x 100%
= 8/25 x 100%
= 32%
Answer: (a)

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Express these ratios in their simplest form: (a) 2 to 10. (b) 80 to 20 (c) 1.Math Exerciseswww.emathematics.net/‎Revise your understanding of proportional reasoning in maths. Here you will find exercises on ratios and proportions, direct proportions, inverse proportions, ...Ratios and Proportions Exercises - Mathematics - About.commath.about.com/od/Ratios-Proportions-Exercises/‎Exercises for Ratios and Proportions. Exercises involving Ratios and Proportions. Proportions Word Problems Worksheet 2. A proportion is a set of 2 fractions ...Ratios and Proportions Math Worksheets! - edHelper.comedhelper.com/ ratios.htm‎Proportions: State whether the ratios are proportional (fractions) · Proportions: State whether the ratios are proportional (mixed ways of writing ratios)BBC - GCSE Bitesize: Ratioswww.bbc.co.uk › Home › Maths › Number‎A secondary school revision resource for GCSE Maths about foundation level fractions, decimals and ratios.Searches related to ratio exercises mathhow to get ratiosmaths ratio and proportion exercisesratio worksheetsequivalent ratios worksheetratio and proportion worksheetratio problems worksheetratio sheetssimple ratio worksheetsRatios and Proportions Exercises - Mathematics - About.commath.about.com/od/Ratios-Proportions-Exercises/‎Exercises for Ratios and Proportions. Exercises involving Ratios and Proportions. Proportions Word Problems Worksheet 2. 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Problem and Solution: Part 3 (Ratio, Proportion, Rate & Partnership)

Question: 17 If Marie has twice as much money as Curie has, who has three times as much money as Sunny has. What is the ratio of the amount of money Sunny has to the amount of money Marie has?
 
Option: (a) 1:8 (b) 1:6 (c) 1:4 (d) 1:2 (e) 2:1

Explore : Let, Sunny hat $ X
:. Curie has $ 3X
:. Marie has $ (3X x 2) or $ 6X
:. The ratio of amount of money Sunny has to the amount of money Marie has
= X:6X = X/6X = 1/6 = 1:6
Answer: (b)

Question: 18Masum has twice as much money as Selim and Selim has 50% more money than what Babal has. If the average money with them is $ 110, then determine the amount of Masum's Money.

Explore: Let, Babal has $ X :. Selim has $ (X + X x 50%) = $ (X x 0.5%X) = $1.5X :. Masum has $ (1.5X x 2) = $3X According to the question,      X + 1.5X + 3X = 110 x 3 => 5.5X = 330 => X = 3.30/5.5 = 60 :. Masum has $ (3 x 60) = $ 180 Answer: $ 180

Question: 19 The cost of a book is 1.5 times that of a CD. The price of a pencil is 1/3 rd of that of a pen, The cost of the pen is twice as much as that of the CD. What is the ratio of cost of the book to cost of the pencil?
Explore: Let, the cost of CD =X
:. Cost of a book = 1.5X
Cost of a pen = 2X
?Cost of a pencil = 2X x 1/3 = 2X/3
:. The ratio of cost of the book to the cost of the pencil
= 1.5X :2X/3 = 1.5X/(2X/3) = 1.5X x 3/2X
= 4.5/2 = 9/4 = 9:4
Answer: 9 : 4

Question: 20 A room has a floor area of 150sq. feet. If the length & breath of the room are in the ratio 3:2, then what is the length of the floor in feet?
Option: (a) 10 (b) 15 (c) 20 (d) 9 (e) None

Explore: Let, L be the length of the room
According to the problem,
length/ width = 3/2
Or, L/width = 3/2 => width 2L/3
:. L x 2L/3 = 150
=> LxL = (3 x 150)/2 = 3 x 3 x 25
:. L 3 x 5 = 15
Answer: (b)

Question: 21 A gentleman spends 2/5th of his monthly income on food, 1/4th on education and the rest $ 200 is saved. What is his monthly income?
Option: (a) 2000 (b) 1500 (c) 1200 (d) 1000 (e) None

Explore: Let, X be his monthly income.
:. (2/5)X  + (1/4)X + 200 = X
:. 200 = X - (2/5)X - (1/4)X
= X (1-2/5 -1/4)
= X((20-8-5)/20) = X(7/.20)
:. X = (200 x 20)/7 571.43
Answer: (e)

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Ratio, Proportion & Partnership: (part 2 )Exercise Problem & solved examples

Question: 10 Given (P + 7Q)/4P = 19/20, what is the ratio of Q:P?
Option: (a) 1:2 (b) 1:3 (c) 2:4 (d) 2:5 (e) 2:7

Explore: (P + 7Q)/4P = 19/20
=> 20P + 140Q = 76P
=> 140Q = 56P
=> P/Q = 140/56 = 5/2
=> P:Q = 5:2
:. Q:P = 2:5

Answer: (d)

Question: 11 Nine years ago the age of P and Q| were in the ratio of 2:3. After 7 years, the ratio of their age will be 3:4. What is the present age of P?

Explore: Let 9 years ago the age of P and Q were 2x & 3x respectively.
:. Present age of P = 2x + 9 
Present age of Q = 3x + 9
According to the question,
(2x +9+7):(3x+9+7) = 3:4
=> (2x+16)/(3x+16) = 3/4
=> 4(2x+16) = 3(3x +16)
=> 8x + 64 = 9x +48
=> 9x-8x = 64 - 48
=> x = 16
:. Present age of P = 2 x 16 + 9 = 41
Answer: 41

Question: 12 Age of three persons are now in the proportion 2:3:4 and in 5 years from now, the proportion will be 5:7:8. What is the present age of the youngest person?
Option: (a) 30 (b) 25 (c) 20 (d) 15 (e) None

Explore: The ratio of the age of the three persons is 2:3:4. So, their age can be 2X, 3X, 4X, where X is any number.
After 5 years their age ratio is given by 5:7:8. So, their age may be 5Y, 7Y & 8Y where Y is any other number.
So, we can write
2X+5 = 5Y .......(1)
3X+5 = 7Y .......(2)

(2) - (1) gives X = 2Y
Or, Y = 1/2
Replacing this value in (1)
2X +5 = (5/2)X
Or, 5 = ((5/2) - 2)X = (1/2)X
:. X = 10
:. Required age 2X = 2x10 = 20
Answer: (c)

Question: 13 A fruit salad mixture consists of apples, peaches and grapes in the ratio 6:5:2 respectively, by weights. If 39 pounds of the mixture is prepared, the mixture includes how many more pounds of apples than grapes?

Explore: In the mixture of 39 pounds,
ratio of apples, peaches & grapes = 6:5:2
:. Weight of apples = 39 x (6/(6+5+2)) = 39 x (6/13) = 18 Pounds
Weight of peaches = 39 x (5/13) = 15 Pounds
Weight of grapes = 39 x (2/13) = 6 Pounds
:. Weight of apples is (18 - 6) or 12 pounds more than grapes.
Answer: 12 pounds

Question: 14 Jahirul and Jalil agree to form a partnership. The partnership agreement requires that Jahirul invest $7,000 less than one half of what Jalil invests. If the total investment is $ 1,25,000 how much does Jalil invest?

Explore: Let, Jalil invest $X
:. Jahirul invests $ (X/2) - 7000
According to the question,
X+(X/2) - 7000 = 125000
=> (2X+X)/2 = 125000+7000
=> 3X/2 = 132000
:. X = (132000 x 2)/3
=> X = 88000
Answer: Jalil invests $ 88000

Question: 15 Arif, Babu and Salm started a business jointly with a total amount of $28000. Arif paid $ 4500 more than Babu and Babu paid $7000 less than Salam. If the company made a profit of $5600, how much profit should Babu receive?

Explore: Let Babu paid $X
:. Arif paid $(X+4500)
Salam paid $(X+7000)
According to the question,
X+X+4500+X+7000 = 2800
=> 3X + 11500 = 28000
=> 3X = 28000 - 11500
=> X = (16500/3) = 5500
:. Babu paid $ 5500
Arif paid $ (5500+4500) = $10000
Salam paid $ (5500 + 7000) = $12500
They will share profit according to the money they paid.
:. Ratio of money paid by Babu, Arif and Salam
= 5500:10000:12500
= 55:100:125
= 11:20:25
Some of the ratio = 11+20+25 = 56
:. Babu received from the profit of $5600
= $5600 x (11/56)
= $1100
Answer: $1100

Question: 16 Arif, Babu and Salam started a business jointly with a total amount of $280. Arif paid $45 more than Babu and Babu paid $70 less than Salam. If the company made a profit of $56, how much profit should Babu receive?
Option: (a) 22 (b) 20 (c) 25 (d) 27 (e) None

Explore: Let, Babu's investment be $B
:. Arif's investment is $(B+45)
And Salam's investment $ (B+70)
According to the problem,
b+(b+45)+(b+70) = 280
=> 3B = 280 -115 = 165
:. B = 55
Since the profit is shared in proportion of capital investment, so,
Babu's profit = ((Babu's capital)/(Total capital)) x Total profit = ((55)/(250)) x 56 = $11
Answer: (e)

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Ratio, Proportion & Partnership: Exercise Problem & solved examples

Question: 1 The ratio of 1/5 to 2/7 is:
Option: (a) 3:5 (b) 5:7 (c) 7:9 (d) 7:10 (e) 3:7

Explore: The ratio of 1/6 to 2/7
= 1/5:2/7
= (1/5)/()2/7
= 1/5 x 7/2
= 7/10
= 7: 10
Answer: (d)

Question: 2 The ratio of 1/4 to 3/5 is
Option: (a) 1 to 3 (b) 3 to 20 (c) 5 to 12 (d) 3 to 4 (e) 5 to 5

Explore: 1/4 to 3/5 = 1/4:3/5 = (1/4)/(3/5) = 5/12
Answer: (c)

Question: 3 A:B = 4:5, A:C = 10:9, then A:B:C = ?
Option: (a) 4:5:9 (b) 4:5:10 (c) 8:9:10 (d) 8:9:10 (e) 20:25:18

Explore: A:B = 4:5
=> B:A = 5:4
=> B:A = 5:5 x 4:5 = 25:20
A:C = 10:9
=> A:C = 10x2:9x2 = 20:18
:. B:A:C = 25:20:18
:. A:B:C = 20:25:18
Answer: (e)

Question: 4 If A:B = 1:2, B:C = 4:3, & A+B+C = 450. What is the value of B?
Explore: A:B = 1:2 = 1x2:2x2 = 2:4
B:C = 4:3
:.  A:B:C = 2:4:3
Sum of the numbers = 2+4+3 = 9
:. Value of B = 450x(4/9) = 200
Answer: 200

Question: 5 Let, X:Y = 3:4 and X:Z = 6:5, then Z:Y =?
Option: (a) 5:3 (b) 6:7 (c) 4:2 (d) 5:4 (e) 5:8

Explore: X:Y = 3:4
=> Y:X = 4:3 => Y:X = 4x2:2x3 = 8:6
Again, X:Z = 6:5
:. Y:X:Z =8:6:5
:. Z:Y = 5:8
Answer: (e)

Question: 6 If X:Y = Y:Z = 1.5 and Z = 2, what is the value of X?
Option: (a) 3 (b) 4 (c) 4.5 (d) 2.5 (e) 5

Explore: Y:Z = 1.5 or Y/Z = 1.5
Or, Y = 1.5Z = 1.5x2 = 3
Now, Z:Y = 1.5
:. X = 1.5Y = (3/2)3 = 9/2 = 4.5
Answer: (c)

Question: 7 If X is 2/5 of Y and Y is 5/7 of Z, what is the ratio of Z:X?
Explore: According to the question,
X = 2Y/5 & Y = 5Z/7
=> X = 2/5 x 5Z/7
=> X = 2Z/7
=>Z/X = 7/2 = 7:2
Answer: 7:2

Question: 8 In a school, the ratio of boys to girls is 3 to 7. If there are 150 boys and girls in the school, how many boys are there?
Option: (a) 45 (b) 75 (c) 90 (d) 105

Explore: The ratio of boys to girls = 3:7
Sum of the ratio = 3 + 7 = 10
No. of boys = 150 x 3/10 = 45
Answer: (45)

Question: 9 The ratio of girls to boys in a class is 3:4. The number of students in the class could be any of the following except:
Option: (a) 35 (b) 28 (c)48 (d) 42

Explore: Since ratio of girls to boys is 3:4 and no. of student can't be fraction and must be divisible by 7(3+4), so, 35, 28 & 42 are divisible by 7.
But 48 is not divisible by 7.

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