Question

answer this question with full explanation with working properly
options r given​

Answer 1

Answer:

(B)3

Step-by-step explanation:

Let, the cost of 1 pencil =x

the cost of 1 pen = y

the cost of 1 book = z

According to the Hypothesis,

7 pencils, 5 pens and 2 books costs Rs. 39

7x+5y+2z = 39 -----------(1)

5 pencils , 3 pens and 4 books costs Rs. 39

5x+3y+4z = 39 -----------(2)

3 pencils, 5pens and 7 books costs Rs.56

3x+5y+7z = 56 -----------(3)

From (1) and (2),

7x+5y+2z = 5x+3y+4z

7x-5x +5y-3y +2z -4z= 0

2x+2y-2z = 0

x + y -z = 0 ------(4)

From (3) and (4)

eq.(3) x 1

eq.(4) x 3

3x+5y+7z = 56

3x+3y -3z = 0

-- -- +

________________

2y+10z = 56

y+5z = 23 ----------(5)

Here, (18,1) ,(13,2),(8,15) and (3,4) are the values satisfied for..y and z of equation 5

But, only the value y = 3 and z = 4 satisfies the eq.(1) ,(2) and (3)

Therefore, y = 3

Hence, cost of each pen = Rs.3

Hope it helps..

Answer 2

Hey !

______________________________

ʟᴇᴛ, ᴛʜᴇ ᴄᴏsᴛ ᴏғ 1 ᴘᴇɴᴄɪʟ =x

ʟᴇᴛ, ᴛʜᴇ ᴄᴏsᴛ ᴏғ 1 ᴘᴇɴᴄɪʟ =xᴛʜᴇ ᴄᴏsᴛ ᴏғ 1 ᴘᴇɴ = ʏ

ʟᴇᴛ, ᴛʜᴇ ᴄᴏsᴛ ᴏғ 1 ᴘᴇɴᴄɪʟ =xᴛʜᴇ ᴄᴏsᴛ ᴏғ 1 ᴘᴇɴ = ʏᴛʜᴇ ᴄᴏsᴛ ᴏғ 1 ʙᴏᴏᴋ = ᴢ

ᴀᴄᴄᴏʀᴅɪɴɢ ᴛᴏ ᴛʜᴇ ǫᴜᴇsᴛɪᴏɴ,

7 ᴘᴇɴᴄɪʟs, 5 ᴘᴇɴs ᴀɴᴅ 2 ʙᴏᴏᴋs ᴄᴏsᴛs ʀs. 39

7x+5ʏ+2ᴢ = 39 -----------(1)

5 ᴘᴇɴᴄɪʟs , 3 ᴘᴇɴs ᴀɴᴅ 4 ʙᴏᴏᴋs ᴄᴏsᴛs ʀs. 39

5x+3ʏ+4ᴢ = 39 -----------(2)

3 ᴘᴇɴᴄɪʟs, 5ᴘᴇɴs ᴀɴᴅ 7 ʙᴏᴏᴋs ᴄᴏsᴛs ʀs.56

3x+5ʏ+7ᴢ = 56 -------(3)

ғʀᴏᴍ (1) ᴀɴᴅ (2),

7x+5ʏ+2ᴢ = 5x+3ʏ+4ᴢ

7x-5x +5ʏ-3ʏ +2ᴢ -4ᴢ= 0

2x+2ʏ-2ᴢ = 0

x + ʏ -ᴢ = 0 ------(4)

ғʀᴏᴍ (3) ᴀɴᴅ (4)

ᴇǫ.(3) x 1

ᴇǫ.(4) x 3

3x+5ʏ+7ᴢ = 56

3x+3ʏ -3ᴢ = 0

-- -- +

________________

2ʏ+10ᴢ = 56

ʏ+5ᴢ = 23. ----------(5)

ʜᴇʀᴇ, (18,1) ,(13,2),(8,15) ᴀɴᴅ (3,4) ᴀʀᴇ ᴛʜᴇ ᴠᴀʟᴜᴇs sᴀᴛɪsғɪᴇᴅ ғᴏʀ..ʏ ᴀɴᴅ ᴢ ᴏғ ᴇǫᴜᴀᴛɪᴏɴ 5

ʙᴜᴛ, ᴏɴʟʏ ᴛʜᴇ ᴠᴀʟᴜᴇ ʏ = 3 ᴀɴᴅ ᴢ = 4 sᴀᴛɪsғɪᴇs ᴛʜᴇ ᴇǫ.(1) ,(2) ᴀɴᴅ (3)

ᴛʜᴇʀᴇғᴏʀᴇ, ʏ = 3

ʜᴇɴᴄᴇ, ᴄᴏsᴛ ᴏғ ᴇᴀᴄʜ ᴘᴇɴ = ʀs.3

______________________________

Thanks !