Question

Sum of two numbers is 103. If greater number is divided by smaller number then the quotient is 2 and the remainder is 19. Then find the numbers.​

Answer 1

❍ Let's say, the greater number be x and the smaller number be y respectively.

By given C O N D I T I O N :

Case – I)

• The sum of both greater and smaller number is 103.

Therefore,

➠ x + y = 103 ⠀⠀⠀⠀⠀⠀ —eq( I ).

⠀⠀⠀⠀⠀⠀

Also,

⠀⠀⠀⠀⠀⠀

Case – II)

• If the greater number is divided by the smaller number then the Quotient is 2 and the Remainder is 19.

Therefore,

➠ x = 2y + 19 ⠀⠀⠀⠀⠀⠀ —eq( I I ).

⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀

⟫ Substituting eq ( II ) in eq ( I ) :

⠀⠀⠀⠀⠀⠀

$:\implies\sf x + y = 103 \\\\\\:\implies\sf 2y + 19 + y = 103 \\\\\\:\implies\sf 3y = 84\\\\\\:\implies\sf y = \cancel\dfrac{84}{3} \\\\\\:\implies\underline{\boxed{\frak{\pmb{\purple{y = 28}}}}}\;\bigstar$

⠀⠀⠀⠀⠀⠀

⟫ Now, from eq ( II ) :

⠀⠀⠀⠀⠀⠀

$:\implies\sf x = 2y + 19\\\\\\:\implies\sf x = 2(28) + 19 \\\\\\:\implies\sf x = 56 + 19\\\\\\:\implies\underline{\boxed{\frak{\pmb{\purple{x = 75}}}}}\;\bigstar$

⠀⠀⠀⠀⠀⠀

$\therefore{\underline{\textsf{Hence,~Greater~number~is~\textbf{75}\;\&\; smaller~number~is~\textbf{28} \sf{respctively.}}}}$

⠀⠀⠀⠀⠀⠀

$\rule{250px}{.3ex}$

V E R I F I C A T I O N :

• It is given that, the sum of both greater and smaller number is 103. So, let's verify :

⠀⠀⠀⠀⠀⠀

Therefore,

⠀⠀⠀⠀⠀⠀

$\dashrightarrow\sf Greater\;no. + Smaller \;no. = 103 \\\\\\\dashrightarrow\sf x + y = 103 \\\\\\\dashrightarrow\sf 75 + 28 = 103\\\\\\\dashrightarrow\boxed{\frak{\pmb{\pink{103 = 103}}}}$

⠀⠀⠀⠀⠀⠀

$\qquad\quad\therefore{\underline{\textsf{\textbf{Hence, Verified!}}}}$

⠀⠀⠀

Answer 2

Answer:

• 75 and 28

Step-by-step explanation:

Given

• Sum of two numbers = 103
• If greater number if divided by smaller number.
• Quotient = 2
• Remainder = 19

To find

• The numbers

Solution

↪ Let the numbers be x and y and y is greater among them.

↪ If greater number if divided by smaller number,

• y/x

↪ Quotient,

• 2

↪ Remainder,

• 19

We know,

• Dividend = Divisor × Quotient + Remainder

We get,

• y = 2x + 19

ATP,

• Sum of two numbers = 103
• x + 2x + 19 = 103
• 3x + 19 = 103
• 3x = 103 - 19
• 3x = 84
• x = 84/3
• x = 28

Hence , the value of x is 28.

Now,

• x + y = 103
• 28 + y = 103
• y = 103 - 28
• y = 75

Hence, the greater number (y) = 75

and, the smaller number (x) = 28