Question

the sum of the digits of two digits number is 7. if the digits are reversed the new number increases by 3 less than 4 times the original number ​

Answer 1

Answer:-

Original number $\large\leadsto\boxed{\sf\purple{16}}$

• Given:-

Sum of the digits of two digit number = 7

When the digits are reversed the new number increases by 3 less than 4 times the original number.

• To Find:-

The original number= ?

• Solution:-

Let the number be 10x + y.

ATQ,

✧ x + y = 7

$\implies\bf{x = 7 - y}$$\: \: \longrightarrow\bf\red{[eqn.1]}$

Reversing the digits:-

✧ $\bf\pink{10y + x}$

According to the question:-

→ $\sf{10y + x + 3 = 4(10x+y)}$

→ $\sf{10y + x + 3 = 40x + 4y}$

→ $\sf{10y - 4y + 3 = 40x - x}$

→ $\sf{6y + 3 = 39x}$

→ $\sf{39x - 6y = 3}$

Substituting the value of [eqn.1]:-

→ $\sf{39(7-y) - 6y = 3}$

→ $\sf{273 - 39y - 6y = 3}$

→ $\sf{273 - 45y = 3}$

→ $\sf{45y = 273 - 3}$

→ $\sf{45y = 270}$

→ $\sf{y = \dfrac{270}{45}}$

$\implies\boxed{\bf\red{y = 6}}$

Substituting this value of y in [eqn.1]:-

✧ $\bf\pink{x = 7-y}$

→ $\sf{x = 7 - 6}$

$\implies\boxed{\bf\red{x = 1}}$

Therefore,

The original number is

✧ $\bf\pink{10x +y}$

→ 10(1) + 6

→ 10 + 6

$\huge\leadsto\boxed{\sf\green{16}}$

Answer 2

Answer:

✡ Given ✡

$\leadsto$ The sum of the two digit number is 7.

$\leadsto$ If the digits are reversed then the new number will be increases by 3 less than 4 times.

✡ To Find ✡

$\leadsto$ What is the original number.

✡ Solution ✡

✏ Let the unit's place be x

✏ And the ten's place be y

⬛ Then the original number be 10x + y

$\mapsto$ The sum of digits is 7

$\implies$ x + y = 7 ...... (1)

Then,

$\implies$ 10y + x = 4(10x + y) - 3

$\implies$ 10y + x = 40x + 4y - 3

$\implies$ 39x - 6y = 3

$\implies$ 13x - 2y = 1 ..... (2)

➡ Multiplying equation (1) by 2 we get,

$\implies$ 2x + 2y = 14 ..... (3)

➡ Adding equation (2) and (3) we get,

$\implies$ 15x = 15

$\mapsto$ x = 1

$\mapsto$ y = 6

Hence, the original number ,

$\implies$ 10x + y = 10(1) + 6

$\implies$ 16

$\therefore$ The original number will be 16.

Step-by-step explanation:

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