Answer the questions on the basis of the information given below.

In a school when a survey is conducted on liking of subjects out of three subjects physics, chemistry mathematics then outcome is as follow.

Total number of students who like physics, chemistry and mathematics is 30, 40, 50 respectively. 10 students shown interest in all three subjects, Number of students who like physics and mathematics both is equal to number of students who like chemistry and mathematics both and is equal to 3/4 times number of students who like physics and chemistry both 15 students like only chemistry.

When class teacher saw this survey report he told head master that at least 20% and at max 40% of those who told they like physics are liars about physics liking. Same percentage for chemistry is 40% to 50%.

Further class teacher added that the liars must belong to those who like only 1 subject and if numbers of liars is more then it belongs to those who like 2 subjects and probability that the who likes all three subjects is a liar is negligible.

1. According to survey what is the ratio of number of students who like only Physics to those who like only Chemistry to those who like only Maths.

Correct Option - 1


Detailed Solution:

From the given condition g = 10,

Number of students who like both Physics and Maths = 10 + f

Number of students who like both chemistry and Maths = 10 + e

From given condition 10 + f = 10 + e or e = f

Similarly from 3^rd condition ¾ (10 + e) = 10 + d

Or 30 + 3e = 40 + 4d

Or

 Since 15 students like only chemistry hence b = 15

Number of students who like only chemistry is 40

Hence e + g + d + b = 40

or e + 10 + (3e – 10)/4 + 15 = 40

or (7e – 10)/4 = 15 or 7e = 70 or e = 10

Hence a = 5, c = 20, f = e = 10, d = 5

Hence the distribution is as follows

As per the observation of  class teacher actual numbers of students who like Physics in

...more

From the given condition g = 10,

Number of students who like both Physics and Maths = 10 + f

Number of students who like both chemistry and Maths = 10 + e

From given condition 10 + f = 10 + e or e = f

Similarly from 3^rd condition ¾ (10 + e) = 10 + d

Or 30 + 3e = 40 + 4d

Or

 Since 15 students like only chemistry hence b = 15

Number of students who like only chemistry is 40

Hence e + g + d + b = 40

or e + 10 + (3e – 10)/4 + 15 = 40

or (7e – 10)/4 = 15 or 7e = 70 or e = 10

Hence a = 5, c = 20, f = e = 10, d = 5

Hence the distribution is as follows

As per the observation of  class teacher actual numbers of students who like Physics in 18 – 24 that means number of students those who lied about their liking of Physics  is 6 to 12 out  of these 6 – 12 students 5 students must be those who liked only Physics. Remaining 1 to 7 students must be from d or f (as g = 10 students assumed that they are not liar)

Let x = actual number of students who like only Physics and chemistry not Maths.

And y = actual number of students who like only Physics and Maths not chemistry.

Similarly z = actual number of students who like only Maths and chemistry not Physics.

Hence from the given condition 1? x + y? 7

And 1? y + z? 5

From the survey report a  = 5, b = 15, c = 20 and required ratio is 1 : 3 : 4

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<p>From the given condition g = 10, </p><p>Number of students who like both Physics and Maths = 10 + f</p><p>Number of students who like both chemistry and Maths = 10 + e</p><p>From given condition 10 + f = 10 + e or e = f</p><p>Similarly from 3^rd condition ¾ (10 + e) = 10 + d</p><p>Or 30 + 3e = 40 + 4d</p><p>Or</p><p>&lt;!- [if gte mso 9]>&lt;xml&gt; <o:OLEObject Type="Embed" ProgID="Unknown" ShapeID="_x0000_i1025" DrawAspect="Content" ObjectID="_1815999878"> </o:OLEObject>&lt;/xml&gt;&lt;! [endif]-&gt;</p><p>&nbsp;Since 15 students like only chemistry hence b = 15</p><p>Number of students who like only chemistry is 40</p><p>Hence e + g + d + b = 40</p><p>or e + 10 + (3e – 10)/4 + 15 = 40</p><p>or (7e – 10)/4 = 15 or 7e = 70 or e = 10</p><p>Hence a = 5, c = 20, f = e = 10, d = 5</p><p>Hence the distribution is as follows</p><div class="photo-widget-full"><div class="figure"><picture><source srcset="" media=" (max-width: 500px)"><img src="https://images.shiksha.com/mediadata/images/1754474646php7DgMRX.jpeg" alt="" width="477" height="285" loading="lazy"></picture></div></div><p>As per the observation of&nbsp; class teacher actual numbers of students who like Physics in 18 – 24 that means number of students those who lied about their liking of Physics&nbsp; is 6 to 12 out&nbsp; of these 6 – 12 students 5 students must be those who liked only Physics. Remaining 1 to 7 students must be from d or f (as g = 10 students assumed that they are not liar)</p><p>Let x = actual number of students who like only Physics and chemistry not Maths.</p><p>And y = actual number of students who like only Physics and Maths not chemistry.</p><p>Similarly z = actual number of students who like only Maths and chemistry not Physics.</p><p>Hence from the given condition 1? x + y? 7</p><p>And 1? y + z? 5</p><div class="photo-widget-full"><div class="figure"><picture><source srcset="" media=" (max-width: 500px)"><img src="https://images.shiksha.com/mediadata/images/1754475486phpyBmB42.jpeg" alt="" width="568" height="373" loading="lazy"></picture></div></div><p>From the survey report a&nbsp; = 5, b = 15, c = 20 and required ratio is 1 : 3 : 4</p>

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