Question

A two digit number mis obtained by multiplying the
sum of the digits by 8. Also, it is obtained by
multiplying the difference of the digits by 14 and
adding 2. Find the number

Answer 1

EXPLANATION.

• GIVEN

A two digit number is obtained by multiply

the sum of digit by 8

it is also obtained by multiply the difference of the digit by 14 and adding 2

Find the number,

According to the question,

Let the two digit number be = 10x + y

Two digit number is obtained by multiply the

sum of digit by = 8

10x + y = 8 ( x + y)

10x + y = 8x + 8y

2x = 7y ....(1)

Two digit number is obtained by multiply the

difference by 14 and adding 2

10x + y = 14 ( x - y) + 2

10x + y = 14x - 14y + 2

- 4x + 15y = 2 .....(2)

From equation (1) and (2) we get,

2x = 7y

x = 7y / 2 ..... (3)

put the value of x in equation (2)

$\bold{- 4( \frac{7y}{2} ) + 15y = 2}$

- 14y + 15y = 2

y = 2

put the value of y = 2 in equation (3)

we get,

x = 7 X 2 / 2

x = 7

Therefore,

The number is = 10x + y

10(7) + 2 = 72

The number is = 72

Answer 2

$\huge\sf\pink{Answer}$

☞ The Number is 72

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$\huge\sf\blue{Given}$

✭ Sum of digits is 8

✭ It is obtained by multiplying the Difference of the digits by 14 and adding 2

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$\huge\sf\gray{To \:Find}$

◈ The Number?

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$\huge\sf\purple{Steps}$

Let the 2 digit number be 10x + y

☯ $\underline{\sf As \ Per \ the \ Question}$

➝ $\sf 10x+y = 8(x+y)$

➝ $\sf 10x+y = 8x+8y$

➝ $\sf 10x-8x = 8y-y$

➝ $\sf 2x = 7y$

➝ $\sf x = \dfrac{7y}{2} \:\:\:\: -eq(1)$

Also given that,

➢ $\sf 10x+y = 14(x-y)+2$

➢ $\sf 10x+y = 14x-14y+2$

➢ $\sf 10x-14x = -14y-y+2$

➢ $\sf -4x = -15y+2$

➢ $\sf -4x+15y = 2 \:\:\: -eq(2)$

Substituting the value of x from eq(1) in eq(2)

➠ $\sf -4(\dfrac{7y}{2})+15y = 2$

➠ $\sf -14y+15y = 2$

➠ $\sf \red{y = 2}$

Substituting the value of y in eq(1)

➳ $\sf x = \dfrac{7y}{2}$

➳ $\sf x = \dfrac{7(2)}{2}$

➳ $\sf \green{x = 7}$

Hence the number is,

»» $\sf 10(7)+2$

»» $\sf 70+2$

»» $\sf \orange{Number = 72}$

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