3 Mark Question

Question 13 Marks

Two numbers are in the ratio 2 : 7. 11 the sum of the numbers is 810. Find the numbers.

Answer

Two numbers are in the ratio = 2 : 7Sum of the numbers = 810
We have,
Sum of the terms in the ratio = 2 + 7 = 9
First number $=\frac29\times810$
$=2\times90$
$=180$
Second number $=\frac{7}{9}\times810$
$=7\times90$
$=630$

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Question 23 Marks

Which ratio is larger in the following pairs?
4 : 7 or 5 : 8

Answer

4 : 7 or 5 : 8L.C.M. of 7 and 8 is 56
$4:7=\frac{5\times8}{7\times8}$
$=\frac{32}{56}$
$5:8=\frac{5\times7}{8\times7}$
$=\frac{35}{56}$
$\frac{35}{56}>\frac{32}{56}$
$\frac58>\frac47$
$5:8>4:7$

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Question 33 Marks

The ratio of income to the expenditure of a family is 7 : 6. Find the savings if the income is Rs. 1400.

Answer

The ratio of income and expenditure = 7 : 6
7x = 1400
x = 200
Expenditure = 6x = 6 × 200 = Rs.1200
Savings = Income - Expenditure
= 1400 - 1200
= Rs. 200

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Question 43 Marks

The ages of two persons are in the ratio 5 : 7. Eighteen years ago their ages were in the ratio 8 : 13. Find their present ages.

Answer

Let the required ages be 5x and 7x.18 years ago their age ratios,
$\frac{5\text{x}-18}{7\text{x}-18}=\frac{8}{13}$
$65\text{x}-13\times18=8\times\text{7x}-8\times18$
$65\text{x}-234=56\text{x}-144$
$65\text{x}-56\text{x}=234-144$
$9\text{x}=90$
$\text{x}=10$
Thus the ages are 5x = 5 × 10 = 50 years
7x = 7 × 10 = 70 years.

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Question 53 Marks

Three numbers are in the ratio 2 : 3 : 5 and the sum of these numbers is 800. Find the numbers.

Answer

Given that,
Three numbers are in ratio 2 : 3 : 5
Sum of these number = 800
Sum of the term of the ratio = 2 + 3 + 5 = 10
First number $=\frac{2}{10}\times800$
= 160 Second number $=\frac{3}{10}\times800$
= 240 third number $=\frac{5}{10}\times800$
= 400

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Question 63 Marks

Divide Rs. 1350 between Ravish and Shikha in the ratio 2 : 3.

Answer

We have, Sume of the terms of the ratio = 2 + 3 = 5 Ravish money $=\frac{2}{5}\times1350$$=2\times270$
$=\text{Rs. }540$
Shikha money $=\frac35\times1350$$=3\times270$
$=\text{Rs. }810$

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Question 73 Marks

If two numbers are in the ratio 6 : 13 and their L.C.M is 312, find the numbers.

Answer

Let the required number be 6x and 13x. Then their L.C.M. is 78x.$78\text{x}=312$
$\text{x}=\frac{312}{78}$
$\text{x}=4$
Thus, The numbers are$6\text{x}=6\times4=24$
$13\text{x}=13\times4=54$

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Question 83 Marks

Which ratio is larger in the following pairs?
15 : 16 or 24 : 25

Answer

15 : 16 or 24 : 25Now L.C.M. of 16 and 25 is 400
We have,
$15:16=\frac{15\times25}{16\times25}$
$=\frac{375}{400}$
$24:25=\frac{24\times16}{25\times16}$
$=\frac{384}{400}$
$\frac{384}{400}>\frac{375}{400}$
$\frac{15}{16}<\frac{24}{25}$

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Question 93 Marks

The ratio of monthly income to the savings of a family is 7 : 2. If the savings be of Rs. 500, find the income and expenditure.

Answer

It is given that,The ratio of income and savings is 7 : 2
Savings
2x = 500
So, x = 250
Therefore,
Income = 7 × 250 = 1750
Expenditure = Income - savings
= 1750 - 500
= Rs. 1250

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Question 103 Marks

The sides of a triangle are in the ratio 1 : 2 : 3. If the perimeter is 36cm, find its sides.

Answer

The sides of the triangle are in the ratio 1 : 2 : 3Sum of the terms in the ratio = 1 + 2 + 3 = 6
Permeter = 36cm
First side $=\frac16\times36$
$=6\text{cm}$
Second side $=\frac26\times36$
$=12\text{cm}$
Third side $=\frac36\times36$
$=18\text{cm}$

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Question 113 Marks

In a class, one out of every six students fails. If there are 42 students in the class, how many pass?

Answer

Given,One out of 6 student fails
x out of 42 students
$16=\frac{\text{x}}{42}$
$\text{x}=\frac{42}{6}$
$\text{x}=7$
Number of students who fail = 7 students
No of students who pass = Total students - Number of students who fail = 42 - 7 = 35 students.

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Question 123 Marks

The scale of a map is 1 : 4000000. What is the actual distance between the two towns if they are 5cm apart on the map?

Answer

The scale of map = 1 : 4000000
Let us assume the actual distance between towns is x cm
1 : 4000000 = 5 : x
x = 5 × 4000000 = 20000000cm
1km = 1000m
1m = 100cm
Therefore
x = 200km

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Question 133 Marks

The ratio of income of a person to his savings is 10 : 1. If his savings for one year is Rs. 6000, what is his income per month?

Answer

The ratio of income of a person to his savings is 10 : 1
Savings per month $=\frac{6000}{12}$
= Rs. 500
Then let income per month be x
x : 500 = 10 : 1
x = 500 × 10
x = 5000

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Question 143 Marks

If x : y = 3 : 5, find the ratio 3x + 4y : 8x + 5y.

Answer

$\text{x}:\text{y}=3:5$$\frac{\text{x}}{\text{y}}=\frac35$
$5\text{x}=3\text{y}$
$\text{x}=\frac{3\text{y}}{5}$
$\text{3x}+\text{4y}:8\text{x}+5\text{y}$
$=\frac{3\times3\text{y}}{5}+4\text{y}:\frac{8\times3\text{y}}{5}+\text{5y}$
$=\frac{9\text{y}+20\text{y}}{5}:\frac{\text{24y}+\text{25y}}{5}$
$=\frac{29\text{y}}{5}:\frac{49\text{y}}{5}$
$=29\text{y}:49\text{y}$
$=29:49$

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Question 153 Marks

If x : y = 8 : 9, find the ratio (7x - 4y) : 3x + 2y.

Answer

$\text{x}:\text{y}=8:9$$\frac{\text{x}}{\text{y}}=\frac89$
$9\text{x}=\text{8y}$
$\text{x}=\frac{8\text{y}}{9}$
$7\text{x}-4\text{y}:3\text{x}+\text{2y}$
$=\frac{7\times\text{8y}}{9}-4\text{y}:\frac{3\times8\text{y}}{9}+2\text{y}$
$=\frac{56\text{y}-36\text{y}}{9}:\frac{\text{42y}}{9}$
$=20:42$
$=10:21$

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Question 163 Marks

The boys and the girls in a school are in the ratio 7 : 4. If total strength of the school be 550, find the number of boys and girls.

Answer

We have,The boys girls is the ratio 7 : 4
Sum of the terms in the ratio = 7 + 4 = 11
Total strength = 550
Boys strength $=\frac{7}{11}\times550$
$=7\times50$
$=350$ boys
Girls strength $=\frac{4}{11}\times550$
$=4\times50$
$=200$ girls

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Question 173 Marks

Which ratio is larger in the following pairs?
9 : 20 of 8 : 13

Answer

9 : 20 or 8 : 13L.C.M. of 20 and 13 is 260
$9:20=\frac{9\times13}{20\times13}$
$=\frac{160}{260}$
$8:13=\frac{8\times20}{13\times20}$
$=\frac{117}{260}$
$\frac{160}{260}>\frac{117}{260}$
$\frac{8}{13}>\frac{9}{20}$

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Question 183 Marks

Give the equivalent ratios of 6 : 8.

Answer

Equivalent ratios of 6 : 8$\frac{6\times2}{8\times2}=\frac{12}{16}$ (By multiplying numerator and denominator by 2)
= 6 : 8
$\frac{\frac62}{\frac82}=\frac{3}{4}=3:4$ (By dividing numerator and denominator by 2)
Two equivalent ratios
3 : 4 = 12 : 16

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Question 193 Marks

Two numbers are in the ratio 7 : 11. If 7 is added to each of the numbers, the ratio becomes 2 : 3. Find the numbers.

Answer

Let the required numbers be 7x and 11x.If 7 is added to each of the numbers it becomes
$\frac{7\text{x}+7}{11\text{x}+7}=\frac23$
$21\text{x}+21=22\text{x}+14$
$\text{x}=21-14=7$
Thus,
The numbers are 7x = 7 × 7 = 49
11x = 11 × 7 = 77

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Question 203 Marks

Which ratio is larger in the following pairs?
3 : 4 or 9 : 16

Answer

3 : 4 or 9 : 16 Now L.C.M. of 4 and 16 is 16 We have,$\frac34$
$=\frac{3\times4}{4\times4}$
$=\frac{12}{16}$ and $\frac{9}{16}=\frac{9}{16}$
Clearly, $12>9$$\therefore\frac{3}{4}>\frac{9}{16}$

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Question 213 Marks

What should be added to each term of the ratio 7 : 13 so that the ratio becomes 2 : 3.

Answer

Let the number to be added be xThen,
$\frac{7+\text{x}}{13+\text{x}}=\frac{2}{3}$
$(7+\text{x})3=2(13+\text{x})$
$3\text{x}-2\text{x}=26-21$
$\text{x}=5$
Hence the required number is 5.

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Question 223 Marks

Divide Rs. 2000 among P, Q, R in the ratio 2 : 3 : 5.

Answer

We have,Sum of the terms of the ratio = 2 + 3 + 5 = 10
P-share $=\frac{2}{10}$ × total mony
$=\frac{2}{10}\times2000$
$=2\times200$
$=\text{Rs. }400$
Q-share $=\frac{3}{10}$ × total money
$=\frac{3}{10}\times2000$
$=3\times200$
$=\text{Rs. }600$
R-share $=\frac{5}{10}$ × total money
$=\frac{5}{10}\times2000$
$=5\times200$
$=\text{Rs. }1000$

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Question 233 Marks

Two numbers are in the ratio 3 : 5. If 8 is added to each number, the ratio becomes 2 : 3. Find the numbers.

Answer

Let the required numbers be 3x and 5x If 8 is added to each other$\text{3x}+8:5\text{x}+8=2:3$
$\frac{3\text{x}+8}{\text{5x}+8}=\frac{2}{3}$
$3(3\text{x}+8)=2(5\text{x}+8)$
$\text{9x}+24=10\text{x}+16$
$10\text{x}-9\text{x}=24-16$
$\text{x}=8$
Thus the numbers are 3x = 3(8) = 24 5x = 5(8) = 40

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Question 243 Marks

Which ratio is larger in the following pairs?
1 : 2 or 13 : 27

Answer

1 : 2 or 13 : 27L.C.M. of 2 and 27 is 54
$1:2=\frac{1\times27}{2\times27}$
$=\frac{27}{54}$
$13:27=\frac{13\times2}{27\times2}$
$=\frac{26}{54}$
$\frac{27}{54}>\frac{26}{54}$
$\frac12>\frac{13}{27}$

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Question 253 Marks

Find the ratio of the price of pencil to that of ball pen, if pencil cost Rs. 16 per score and ball pen cost Rs. 8.40 per dozen.

Answer

One score = 20It is Rs. 16 per score for pencil
Pencil cost $=\frac{16}{20}$
$=\text{Rs. }0.80$
Cost of one dozen ball pen = Rs. 8.40
Cost of one ball pen $\frac{8.40}{12}$
$=\text{Rs. }0.70$
Ratio of peice of pencil to that of ball pen $=\frac{0.80}{0.70}$
$=\frac87$

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Question 263 Marks

The ratio of zinc and copper in an alloy is 7 : 9. It the weight of the copper in the alloy is 11.7kg, find the weight of the zinc in the alloy.

Answer

We have,The ratio of zinc and copper in an alloy = 7 : 9
Weight of copper in the alloy = 11.7kg
$\text{9}\text{x}=11.7\text{kg}$
$\text{x}=\frac{11.7}{9}$
Weight of zinc in the alloy
= 1.3 × 7
= 9.10kg
Therefore weight of zinc = 9.10kg

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Maths 3 Mark Question

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