Question

5. The sum of the digits of a two digit number is 10 and the digit at units place is 2/3rd of the digit
at tens place. Find the number.
​

Answer 1

Answer:

Let the 10s digit of two digit number be x and 1s digit be y

Hence the number is 10x + y

The number of two digits if a two digit number is 10. It means

x + y = 10…Eq.1

The digit at the unit place is 2/3rd of the digit at the tens place

y = 2/3x

y = 2x/3.. Eq .2

Now substituting the value of y from Eq.. 2 to Eq..1

x + y = 10

x + 2x/3 = 10

(3x + 2x)/3 = 10

Cross multiplication

5x = 30

x = 30/5

x = 6

The 10s digit is 6

Substituting value of x in Eq..2 to drive value of y

y = 2x/3

y = 2 × 6/3

y = 2 × 2

y = 4

The 1s digit is 4

Thus the number is 64.

Answer the number is 64

Step-by-step explanation:

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Answer 2

ʟᴇᴛ ᴛʜᴇ ᴛᴡᴏ ᴅɪɢɪᴛ ɴᴜᴍʙᴇʀ ʜᴀᴠᴇ x ᴀs ɪᴛs ᴛᴇɴ's ᴘʟᴀᴄᴇ ᴀɴᴅ ʏ ᴀs ɪᴛs ᴜɴɪᴛ's ᴘʟᴀᴄᴇ sᴏ ᴛʜᴀᴛ ᴛʜᴇ ɴᴜᴍʙᴇʀ ɪs ᴇǫᴜᴀʟ ᴛᴏ $\sf\small{10x\: +\: ʏ}$. ɪᴛ ɪs ɢɪᴠᴇɴ ᴛʜᴀᴛ :-

$\sf\small{x\: +\: y\: = \:10}$

⠀ ⠀⠀ ⠀ $\sf{\bold{1\:equ.}}$ $\sf\small{Also, \:the \:digit\: at\: unit \:place\:is}$$\sf\small{ two\:-\: third\: the }$$\sf\small{digit \:at \:ten's \:place. }$

$\sf\small{So,\: y \:=}\:\frac{ 2}{3}\: x$

⠀ ⠀⠀

⠀ ⠀⠀ ⠀ $\sf{\bold{2\:equ.}}$ $\sf\small{Putting \:this \:value \:of\: y\: in\: (1), }$

$\sf\small{We\: have\: x\:+}$ $\frac{2}{3}$$\sf\small{ x \:=\:10 \:or }$$\frac{5}{3}$ $\sf\small{x \:= \:10\:\:or \: \: x \:= \:6 }$

⠀ ⠀⠀ ⠀ ⠀

$\sf\small{Also, \: y\: =}$ $\frac{2}{3}$ x

= $\frac{2}{3}$$\sf\small{×\:6 }$

= $\sf\small{4 }$

$\sf\small{∴\: x \:= \:6\: and\: y\: = \:4.}$