Question

while preparing for csat paper akshay attempted to solve 3 paper namely quantitative aptitude verbal ability and logical ability each of which have the full marks of 100 it is found that one third of the marks obtain by akshay in logical reasoning is 5 more than half of his marks obtain in verbal ability he has scored a total of 210 marks in the test 70 marks in quantitative aptitude . what is difference between the marks obtained by him in quantitative aptitude and verbal ability. ​

Answer 1

AnswEr :

• 3 Papers of 100 Marks Each
• One third of the marks obtain in logical reasoning is 5 more than half of his marks obtain in verbal ability.
• Total Marks Scored = 210 Marks
• Quantitative Aptitude = 70 Marks
• Find Difference between the marks obtained in quantitative aptitude and verbal ability.

• Let's Head to the Question Now :

⇒ Total Marks = Paper × Marks

⇒ Total Marks = 3 × 100

⇒ Total Marks = 300

$\rule{100}{2}$

↠ Total Marks Obtained = Quantitative Aptitude + Verbal Ability + Logical Ability

↠ 210 = 70 + Verbal Ability + Logical Ability

↠ 210 – 70 = Verbal Ability + Logical Ability

↠ Verbal Ability + Logical Ability = 140

↠ Logical Ability = 140 – Verbal Ability

$\rule{300}{1}$

• According to the Question Now :

$\longrightarrow\tt\dfrac{Logical\:Ability}{3} = 5 + \dfrac{Verbal\:Ability}{2}\\ \\\longrightarrow\tt\dfrac{140 - Verbal\:Ability}{3} = 5 + \dfrac{Verbal\:Ability}{2}\\\\\longrightarrow\tt\dfrac{140 - Verbal\:Ability}{3} = \dfrac{10 + Verbal\:Ability}{2} \\ \\\longrightarrow\tt2(140 - Verbal\:Ability) = 3(10 + Verbal\:Ability) \\ \\\longrightarrow\tt280 - 2Verbal\:Ability = 30 + 3Verbal\:Ability \\ \\\longrightarrow\tt280 - 30= 2Verbal\:Ability + 3Verbal\:Ability \\ \\\longrightarrow\tt250= 5Verbal\:Ability \\ \\\longrightarrow\tt \cancel\dfrac{250}{5} = Verbal\:Ability \\ \\\longrightarrow \purple{\tt Verbal\:Ability=50}$

$\rule{300}{2}$

• Difference between QA and, VA :

↠ Difference = Quantitative Aptitude – Verbal Ability

↠ Difference = ( 70 – 50 ) Marks

↠ Difference = 20 Marks

⠀

∴ Difference between Quantitative Aptitude and Verbal Ability is 20 Marks.

Answer 2

❏ Solution:-

❍ Some important Notations

✦QA $\sf\longrightarrow\bf$ quantitative aptitude.

✦LA $\sf\longrightarrow\bf$ Logical Ability .

✦VA $\sf\longrightarrow\bf$ Verbal Ability

❍ Given:-

✏

• Each paper marks=100
• No. of papers=3
• Total marks=(3×100)=300

✏

• marks in QA=70

✏

$\bf\frac{1}{3}$'rd of the marks obtain by akshay in L.A. is 5 more than $\bf\frac{1}{2}$ of his marks obtain in V.A.

i.e, if we arrange this in equation form then it will be,

$\sf\longrightarrow \bf \frac{1}{3}L.A.=\frac{1}{2}V.A.+5$

$\sf\longrightarrow \bf \frac{1}{3}L.A.-\frac{1}{2}V.A.=5$

$\sf\longrightarrow \bf \frac{2L.A.-3V.A.}{6}=5$

$\sf\longrightarrow \bf 2L.A.-3V.A.=30$

$\sf\longrightarrow\boxed{ \bf 2L.A.=30+3V.A.}............(i)$

✏

• Total marks scored by him=210,

$\sf\longrightarrow\bf \:L.A.+\:V.A. +\:Q.A. =210$

$\sf\longrightarrow\bf \:L.A.+\:V.A. =210-Q.A.$

$\sf\longrightarrow\bf \:L.A.+\:V.A. =210-70$

$\sf\longrightarrow\bf \:L.A.+\:V.A. =140$

[ multiplying by 2 on Both sides ]

$\sf\longrightarrow\bf\boxed{ 2\:L.A. =280-2\:V.A.}...........(ii)$

Now,comparing equation (i) and equation (ii),we get,

$\sf\longrightarrow\bf 30+3\:V.A.= 280-2\:V.A$

$\sf\longrightarrow\bf 3\:V.A.+2\:V.A= 280-30$

$\sf\longrightarrow\bf 5\:V.A= 250$

$\sf\longrightarrow\bf V.A= \frac{\cancel{250}}{\cancel5}$

$\sf\longrightarrow\bf\boxed{ \large{\red{V.A= 50}}}$

NoW, putting the value of V.A.= 50 in equation (I), we get,

$\sf\longrightarrow\bf \:L.A.+\:V.A. =140$

$\sf\longrightarrow\bf \:L.A. =140-\:V.A.$

$\sf\longrightarrow\bf \:L.A. =140-50$

$\sf\longrightarrow\bf \:L.A. =90$

$\sf\longrightarrow\bf\boxed{ \large{\red{L.A= 90}}}$

Hence,

$\sf\bf Solution\begin{cases}</p><p></p><p></p><p>\bf\text{obtained marks in :-} \\</p><p></p><p>\text{Q.A.=70 marks} \\ </p><p>\text{V.A.=50 marks} \\</p><p>\text{L.A.=90 marks} </p><p></p><p>\end{cases}$

∴ Marks difference between Q.A. & V.A. :

=Q.A. - V.A.

=70 - 50

=20 (ans).

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$\underline{ \huge\mathfrak{hope \: this \: helps \: you}}$

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