Question

.The ten digits is 5 more than the units digit.The sum of the digit of a two-digit number is 3 less than one-fifth the number.

Answer 1

The correct answer is -60.

Given:

A number such that the ten's digit is 5 more than the unit's digit.

The sum of the digits of the two-digit number is 3 less than one-fifth of the number.

To Find:

The required number.

Solution:

We have to find a two-digit number such that the ten's digit is 5 more than the unit's digit and the sum of its digits is 3 less than one-fifth the number.

Let us assume that the one place of the two-digit number is 'u' and the tens place is ''.

⇒ The required number = 10t+u

We are given that the ten's digit is 5 more than the unit's digit of this number. The above statement in equation form is:

t = u+5

⇒ t-u = 5 .......................(I)

Also, the sum of its digits is 3 less than one-fifth of the number.  The above statement in equation form is:

t+u = (10t+u)/5 - 3

⇒ 5(t+u) = 10t+u - 15

⇒ 10t+u - 5(t+u) = 15

⇒ 5t -4u = 15 ........................(II)

Multiplying equation (I) by -5, we get

-5t + 5u = -25  ........................(III)

Adding equations (II) and (III), we get:

( 5t -4u) + (-5t + 5u) = 15-25

u = -10

Substituting the above value in equation (I), we have

t-u = 5

⇒ t -(-10) = 5

⇒ t = -5

Hence the required number = 10t+u = 10(-5)+(-10) = -60.

∴ The correct answer is -60.

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Answer 2

Answer:

The required to digit number is -60.

Step-by-step explanation:

Given :

Ten digit is 5 more than the units digit.

Also , the sum of the digit of a two-digit number is 3 less than one-fifth the number.

To find :

The unknown two digit number.

Solution :

Let the units digit be x and tens digit be y

Then as given, ten digits is 5 more than the units digit, so y = x+5 ----eq.(1)

the required number is 10y + x .

Also , the sum of the digit of a two-digit number is 3 less than one-fifth the number.

⇒ y + x =1/5 × (10y + x) -3

⇒5( y + x )= 10 y + x -(3×5)

⇒5y + 5x = 10y + x -15

⇒5x - x = 10y -5y -15

⇒4x =5y - 15 ---------eq.(2)

putting y = x +5 in eq. (2) we get ,

4x = 5(x + 5) - 15

4x = 5x +25 -15

5x - 4x = -25 + 15

x= -10

substituting x= -10 in eq. (1)

Therefore y = x+5  = -10 +5

         y = -5

∴The required  two digit number is

        10y + x = 10×(-5) + (-10) = -50 - 10 = -60.

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