Question

Two students give an examination. One of them secured 9 marks more than the other
and his marks were 56% of the sum of their marks. Find the marks obtained by them.​

Answer 1

Question ⤵

$\Rightarrow$ students give an examination. One of them secured 9 marks more than the other and his marks were 56% of the sum of their marks.

Find the marks obtained by them

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Solution ⤵

Let their marks be (x+9) and x.

Then, x+9 = $\frac{56}{100}$(x + 9 +x)

=> 25(x+9)

=> 14 (2x + 9)

=> 3x = 99

=> x = \cancel \frac{99}{3}

=> x = 33.

$\because$ their marks are 42 and 33 their marks are 42 and 33

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Answer 2

ǫᴜᴇꜱᴛɪᴏɴ :

ᴛᴡᴏ sᴛᴜᴅᴇɴᴛs ɢɪᴠᴇ ᴀɴ ᴇxᴀᴍɪɴᴀᴛɪᴏɴ. ᴏɴᴇ ᴏғ ᴛʜᴇᴍ sᴇᴄᴜʀᴇᴅ 9 ᴍᴀʀᴋs ᴍᴏʀᴇ ᴛʜᴀɴ ᴛʜᴇ ᴏᴛʜᴇʀ ᴀɴᴅ ʜɪs ᴍᴀʀᴋs ᴡᴇʀᴇ 56% ᴏғ ᴛʜᴇ sᴜᴍ ᴏғ ᴛʜᴇɪʀ ᴍᴀʀᴋs. ғɪɴᴅ ᴛʜᴇ ᴍᴀʀᴋs ᴏʙᴛᴀɪɴᴇᴅ ʙʏ ᴛʜᴇᴍ.

ʂᴏᴜʟᴛɪᴏɴ :

ʟᴇᴛ ᴏɴᴇ ᴏғ ᴛʜᴇ sᴛᴜᴅᴇɴᴛs sᴇᴄᴜʀᴇ x ᴍᴀʀᴋs.

ᴛʜᴇɴ, ᴛʜᴇ ᴏᴛʜᴇʀ sᴛᴜᴅᴇɴᴛ sᴇᴄᴜʀᴇs (x+9) ᴍᴀʀᴋs.

ғʀᴏᴍ ᴛʜᴇ ɢɪᴠᴇɴ ᴄᴏɴᴅɪᴛɪᴏɴ, ᴡᴇ ʜᴀᴠᴇ

$\small\green{(x + 9) = 56\% \: ᴏբ \: (x + x + 9) = \frac{56}{100} \times (2x + 9)}$

⇒ 100x + 900 = 112x + 504

⇒ 12x = 900 − 504 = 396

$\small\red{⇒x = \frac{396}{12} } =\huge 33$

ᴛʜᴇʀᴇғᴏʀᴇ, ᴍᴀʀᴋs ᴏʙᴛᴀɪɴᴇᴅ ʙʏ ᴏᴛʜᴇʀ sᴛᴜᴅᴇɴᴛ x + 9 = 33 + 9 = 42 .

ᴍᴀʀᴋs ᴏʙᴛᴀɪɴᴇᴅ ʙʏ ʙᴏᴛʜ sᴛᴜᴅᴇɴᴛs ᴀʀᴇ 33 ᴀɴᴅ 42 .