Question

the difference between increasing a number by 8% and decreasing it by 7% is 75. the number is​

Answer 1

SOLUTION :

• Lᴇᴛ ᴛʜᴇ ʀᴇǫᴜɪʀᴇᴅ ɴᴜᴍʙᴇʀ ʙᴇ x.

• Tʜᴇɴ 8% ᴏғ x = 8x/100

$\longmapsto \sf \: therefore, \: the \: inceased \: number \: \\ \sf = x \: + \dfrac{8x}{100} = \dfrac{108x}{100}$

Sɪᴍɪʟᴀʀʟʏ, Tʜᴇ ɴᴜᴍʙᴇʀ ᴅᴇᴄʀᴇᴀsᴇᴅ ʙʏ 7% =

$\longmapsto \sf \: x - \dfrac{7x}{100} = \dfrac{93x}{100}$

Nᴏᴡ, ᴛʜᴇ ᴅɪғғᴇʀᴇɴᴄᴇ ʙᴇᴛᴡᴇᴇɴ ᴛʜᴇ ɪɴᴄʀᴇᴀsᴇᴅ ᴀɴᴅ ᴅᴇᴄʀᴇᴀsᴇᴅ ɴᴜᴍʙᴇʀs =

$\longmapsto \sf \: \dfrac{108x}{100} - \dfrac{93x}{100} = \dfrac{15x}{100}$

Sɪɴᴄᴇ ᴀᴄᴛᴜᴀʟ ᴅɪғғᴇʀᴇɴᴄᴇ = 75, Tʜᴇʀᴇғᴏʀᴇ

$\longmapsto \sf \dfrac{15x}{100} = 75$

$\longmapsto \sf \: x = \dfrac{{ \cancel{75}} \times 100}{{ \cancel{15}}}$

$\longmapsto \sf \: 5 \times 100 = 500$

$\hookrightarrow {\sf {\boxed {\red{ \frak{the \: required \: number \: is \: 500.}}}}}$

Hᴏᴘᴇ ɪᴛs ʜᴇʟᴘ ʏᴏᴜ~

Answer 2

Answer:

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