Question

In a test, Arjun obtained 9 marks more than Arvind whereas Rakesh obtained 5 m
more than that obtained by Arjun and Arvind. If all of them together obtained 195 marks. Find the marks obtained by each of them.​

Answer 1

⛦ Given :

• Arjun obtained 9 marks more than Arvind
• Rakesh obtained 5 marks more than the marks obtained by Arjun and Arvind.
• Sum of their marks obtained is 195

⛦ To find :

• The marks obtained by these three boys.

⛦ Solution :

•Let's assume Arvind's marks as x

•Then, Arjun's marks will be x + 9

•And marks of Rakesh will be x + x + 9 + 5 = 2x+14

According to Question,

⇒ x + x + 9 + 2x + 14 = 195

⇒ 2x + 2x + 23 = 195

⇒ 4x = 195 - 23

⇒ 4x = 172

⇒ x = 172/4

⇒ x = 43

Therefore,

• Marks attained by Arvind = x = 43
• Marks attained by Arjun = x + 9 = 43 + 9 = 52
• Marks attained by Rakesh = 2x + 14 = 2×43 + 14 = 86 + 14 = 100.

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★ Verification ★

As it is given that the marks obtained by all together is 195.

So,

Marks of Arvind + Marks of Arjun + Marks of Rakesh = 195

Putting the value,

43 + 52 + 100 = 195

95 + 100 = 195

195 = 195

Hence, L.H.S. = R.H.S.

Thus, Verified !

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Answer 2

Required Answer:

• Marks obtained by Arjun = 43
• Marks obtained by Arvind = 52
• Marks obtained by Rakesh = 100

Given :

• In a test, Arjun obtained 9 marks more than Arvind
• Rakesh obtained 5 marks more than the marks obtained by Arjun and Arvind.
• Total marks obtained by them is 195

To find :

• Marks obtained by each of them.

Required Solution :

• Let the mark obtained by Arvind be x
• So then, Arjun's marks will be x + 9
• Rakesh's marks will be x + x + 9 + 5 = 2x + 14

According to the Question,

$\\ \sf \: ➠ \: ( x + x )+ 9 +( 2x) + 14 = 195 \\ \\ \sf \: ➠ \: (2x + 2x )+ 23 = 195 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \sf \: ➠ \: 4 x + 23 = 195 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \sf \: ➠ \: 4x = 195 - 23 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \sf \: ➠ \: 4x = 172 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \sf \: ➠ \: x = \frac{172}{4} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \\ \\ \sf \: ➠ \: x = { \underline{ \boxed{ \bigstar{ \pink{ \bf{43}}}}}} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:$

Hence,

The marks obtained by Arvind => x = 43

The marks obtained by Arjun => x + 9 = 43 + 9 = 52

The marks obtained by Rakesh => 2x + 14 = 2 × 43 + 14 = 86 + 14 = 100

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