Subjective Questions
Q1:
Find the third proportional to 2 and 22.
Type: Short
Difficulty: Easy
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Answer: <p>Solution:</p> <p>Let the required third proportion be x.</p> <p>2 : 22 = 22 : x</p> <p>or, \(\frac{2}{22}\) = \(\frac{22}{x}\)</p> <p>or, 2x = 22\(\times\) 22</p> <p>or, x = \(\frac{22 \times 22}{2}\)</p> <p>\(\therefore\) x = 242</p>
Q2:
Find the mean proportion between 2 and 32.
Type: Short
Difficulty: Easy
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Answer: <p>Solution:</p> <p>Let the required mean proportion be x. Then,</p> <p>2 : x = x : 32</p> <p>or, \(\frac{2}{x}\) = \(\frac{x}{32}\)</p> <p>or, x<sup>2</sup> = 64</p> <p>or, x = \(\sqrt{64}\)</p> <p>\(\therefore\) x = 8</p>
Q3:
Find the fourth proportional to 5, 7 and 8.
Type: Short
Difficulty: Easy
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Answer: <p>Solution:</p> <p>Let x be the proportional to 5, 7 and 8</p> <p>Then, \(\frac{5}{7}\) = \(\frac{8}{x}\)</p> <p>or, 5x =7 \(\times\) 8</p> <p>or, x = \(\frac{56}{5}\)</p> <p>\(\therefore\) x = 11.2</p>
Q4:
Find the value of x in 16 : 8 = x : 5
Type: Short
Difficulty: Easy
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Answer: <p>Solution:</p> <p>16 : 8 = x : 5</p> <p>or, \(\frac{16}{8}\) = \(\frac{x}{5}\)</p> <p>or, 8x =16 \(\times\) 5</p> <p>or, x = \(\frac{80}{8}\)</p> <p>\(\therefore\) x = 10</p>
Q5:
If 7 pencils cost Rs 150, what is the cost of 12 pencils?
Type: Long
Difficulty: Easy
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Answer: <p>Solution:</p> <p>Let the Cost of 12 pencils be Rs x.</p> <p>Since the cost are proportional to the number of pencils, We have</p> <p>\(\frac{7}{150}\) = \(\frac{12}{x}\)</p> <p>Or, 7x = 12 \(\times\)150</p> <p>Or, x = \(\frac{12\times150}{7}\)</p> <p>= 257.14</p> <p>Hence, the cost of 12 pencils = Rs 257.14</p>
Q6:
If 15 pens cost Rs 105, how much will 20 pens cost?
Type: Long
Difficulty: Easy
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Answer: <p>Solution:</p> <p>Let the cost of 20 pens be x.</p> <p>Since the costs are proportional to the number of pens, we have</p> <p>\(\frac{15}{105}\) = \(\frac{20}{x}\)</p> <p>or, 15 x = 20 \(\times\) 105</p> <p>or, x = \(\frac{20 \times 105}{15}\)</p> <p>or, x = \(\frac{2100}{15}\)</p> <p>\(\therefore\) x = 140</p> <p>Hence, the cost of 20 pens is Rs 140.</p> <p></p>
Q7:
Given numbers 7, 9, z, 18. Find z.
Type: Short
Difficulty: Easy
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Answer: <p>Solution:</p> <p>The ratio of first two numbers = \(\frac{7}{9}\)</p> <p>The ratio of second two numbers = \(\frac{z}{18}\)</p> <p>Now,</p> <p>\(\frac{7}{9}\) = \(\frac{z}{18}\)</p> <p>or, z = \(\frac{7\times18}{9}\)</p> <p>or, z = 7\(\times\)2</p> <p>\(\therefore\) z = 14</p> <p></p>
Q8:
Find the value of x.
x:5 = 10:25
Type: Short
Difficulty: Easy
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Answer: <p>Solution:</p> <p>Given, x:5 = 10:25</p> <p>or, \(\frac{x}{5}\) = \(\frac{10}{25}\)</p> <p>or, 25x = 5 \(\times\) 10</p> <p>or, x = \(\frac{50}{25}\)</p> <p>\(\therefore\) x = 2</p> <p></p>
Q9:
Find the value of x.
3:7 = 21:x
Type: Short
Difficulty: Easy
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Answer: <p>Solution:</p> <p>Given, 3:7 = 21:x</p> <p>or, \(\frac{3}{7}\) = \(\frac{21}{x}\)</p> <p>or, x = \(\frac{21\times7}{3}\)</p> <p>\(\therefore\) x = 49</p>
Q10:
Given numbers 3, a, 9, 21. Find a.
Type: Short
Difficulty: Easy
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Answer: <p>Solution:</p> <p>The first two number of ratio = \(\frac{3}{a}\)</p> <p>Second two number of ratio = \(\frac{9}{21}\)</p> <p>given numbers are in proportion, so</p> <p>\(\frac{3}{a}\) = \(\frac{9}{21}\)</p> <p>or, a = \(\frac {3\times21}{9}\)</p> <p>\(\therefore\) a = 7</p>
Q11:
Find the value of x.
25 : 15 = x : 3
Type: Short
Difficulty: Easy
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Answer: <p>Solution:</p> <p>Given,</p> <p>25 : 15 = x : 3</p> <p>or, \(\frac{25}{15}\) = \(\frac{x}{3}\)</p> <p>or, x = \(\frac{25\times3}{15}\)</p> <p>or, x = \(\frac{75}{15}\)</p> <p>\(\therefore\) x = 5</p> <p></p>
Q12:
Check, whether the following numbers form a proportion or not.
7, 8, 14, 20.
Type: Short
Difficulty: Easy
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Answer: <p>Solution:</p> <p>The ratio of first and second numbers = \(\frac{7}{8}\) = 7:8</p> <p>The ratio of third and fourth numbers = \(\frac{14}{20}\) = 7:10</p> <p>Hence, the first ratio 7:8 and the second ratio 14:20 = 7:10 are not not in the proportional form.</p>
Q13:
Find the cost of 23 meters of cloth, if 5 meters of cloth costs Rs 625.
Type: Long
Difficulty: Easy
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Answer: <p>solution:</p> <p>Let, the cost of 23 meters of cloth be x.</p> <p>Since, the costs are proportional to the meters of cloth.</p> <p>\(\frac{5}{625}\) = \(\frac{23}{x}\)</p> <p>or, 5\(\times\)x = 23\(\times\)625</p> <p>or, x = \(\frac{23\times625}{5}\)</p> <p>\(\therefore\) x = 2875</p> <p>Hence, the cost of 23 meters of cloth is Rs 2875.</p>
Q14:
The ratio of the students using pens and pencils in Dharan Higher Secondary School is 10:11. If 110 students are using pencils, find the number of students using pens?
Type: Long
Difficulty: Easy
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Answer: <p>Solution:</p> <p>Ratio of students usingpens and pencils = 10:11</p> <p>Number of students using pencils = 110</p> <p>Number of students using pens =?</p> <p>Let, the number of students using pen be x.</p> <p>According to the question,</p> <p>110:x = 10:11</p> <p>or, \(\frac{110}{x}\) = \(\frac{10}{11}\)</p> <p>or, x = \(\frac{110\times11}{10}\)</p> <p>or, x = 11\(\times\)11</p> <p>\(\therefore\) x = 121</p> <p>Hence, 121 number of students are using pens.</p>
Q15:
The ratio of milk and sugar in a candy is 5:3. If there is 750 gm milk, how much is the sugar?
Type: Long
Difficulty: Easy
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Answer: <p>Solution:</p> <p>Let, the quantity of sugar be x.</p> <p>Quantity of milk= 750 gm</p> <p>The ratio of milk and sugar = 5:3</p> <p>\(\frac{750}{x}\) = \(\frac{5}{3}\)</p> <p>or, x = \(\frac{750\times3}{5}\)</p> <p>\(\therefore\) x = 450</p> <p>Hence, There is 450gm sugar in the candy.</p>
Q16:
The Ratio of the Students passed in first division, Second division and Third division is 2:4:5, among 153 students. If 21 students failed the exam, how many passed in First division, Second division and Third division
Type: Long
Difficulty: Easy
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Answer: <p>Solution:</p> <p>Number of Students participated in the exam = 153</p> <p>Number of Failed Students = 21</p> <p>Total passed students = 153 - 21 = 132</p> <p>The Ratio of 132 students passed in first, second and third division = 2:4:5</p> <p>Now, Number of students passed in First division = 2x</p> <p>Number of students passed in Second division = 4x</p> <p>Number of students passed in Third division = 5x</p> <p>2x+ 4x+ 5x = 132</p> <p>Or, 11x = 132</p> <p>Or, x= \(\frac{132}{11}\) = 12</p> <p>Hence,</p> <p>Number of students passed in First division = 2x = 2\(\times\)12 = 24</p> <p>Number of students passed in Second division = 4x = 4\(\times\)12 = 48.</p> <p>Number of students passed in Third division = 5x = 5\(\times\)12 = 60</p>
Q17:
If the gravitational ratio of Earth and Moon is 1:6. If the weight of an object in Earth is 90N, find it's weight in the Moon ?
Type: Long
Difficulty: Easy
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Answer: <p>Solution:</p> <p>The Gravitational Ratio of Earth and Moon = 1:6</p> <p>Weight of an object in the Earth = 90N</p> <p>Weight of that object in the Moon =?</p> <p>Let, the weight in Moon be xN.</p> <p>Now,</p> <p>\(\frac{xN}{90N}\) = \(\frac{1}{6}\)</p> <p>or, x = 90\(\times\)\(\frac{1}{6}\)</p> <p>\(\therefore\) x = 15N</p> <p>Hence, The weight in Moon is 15N.</p>
Q18:
How much should be added to both the numbers, to make the ratio 3:5 into 5:6 ?
Type: Long
Difficulty: Easy
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Answer: <p>Solution:</p> <p>Let, x be the number to make the ratio 3:5 into 5:6.</p> <p>Now,</p> <p>\(\frac{3 + x}{5 + x}\) = \(\frac{5}{6}\)</p> <p>or, 6( 3 + x) = 5( 5 +x)</p> <p>or, 18 + 6x = 25 + 5x</p> <p>or, 6x -5x = 25 - 18</p> <p>\(\therefore\) x = 7</p> <p>Hence, 7 should be added to both the numbers to make the Ratio3:5 into 5:6.</p>
Q19:
In the marriage ceremony, a cook can cook 20 kg meat in 30 minutes. How much time is required for them to cook 15 kg meat?
Type: Long
Difficulty: Easy
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Answer: <p>Solution:</p> <p>Let, the time required to cook 15 kg meat be x minutes.</p> <p>Now,</p> <p>\(\frac{30}{x }\) = \(\frac{20}{15}\)</p> <p>or, x = \(\frac{30\times15}{20}\)</p> <p>or, x = \(\frac{450}{20}\)</p> <p>\(\therefore\) x = 22.5 minutes</p> <p>Hence, 22 minutes 5 sec is required to cook 15 kg meat.</p>
Q20:
Simran scored in the ratio of 10:12 in Mathematics and Science. If she scored 80 in Science, find the marks she got in Mathematics?
Type: Long
Difficulty: Easy
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Answer: <p>Solution:</p> <p>Let, x be the marks she got in Mathematics.</p> <p>The Ratio of Marks obtained in Mathematics and Science = \(\frac{10}{12}\)</p> <p>Marks in Science = 80</p> <p>Now,</p> <p>\(\frac{x}{80}\) = \(\frac{10}{12}\)</p> <p>or, x = \(\frac{10\times80}{12}\)</p> <p>or, x = \(\frac{10\times20}{3}\)</p> <p>or, x = \(\frac{200}{3}\)</p> <p>\(\therefore\) x = 66\(\frac{2}{3}\)</p> <p>She got 66\(\frac{2}{3}\) in Mathematics.</p>
