Question

There is a number consisting of two digits . The sum of the two digits is 14. If we subtract 29 from the number then the two digits are equal . make the equations and find out the number​

Answer 1

Given :-

• sum of two digits is = 14
• If we subtract 29 from the number then the two digits are equal .

Solution :-

Lets assume That, The given Two digit Number is (10x+y) .

we have now :-

→ x + y = 14 ------- Equation (1)

Now , when we subtract 29 from our original number the digit at both tens and ones place of new number become same . So, Lets Assume That, both Digits of New number are z.

Than,

→ (10x + y) - 29 = (10z + z)

→ (10x + y) - 29 = 11z -------- Equation (2)

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Hence, the digit at tens place of original number will be reduced by 3 and that will be equal to the digit at tens place of new number, which is z.

So,

z = (x - 3) ------------- Equation (3) .

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Putting value of Equation (3) in Equation (2) now,

→ (10x + y) - 29 = 11(x - 3)

→ 10x - 11x + y = - 33 + 29

→ y - x = (-4) -------------- Equation (4).

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Adding Equation (1) & Equation (4) now, we get,

→ (x + y) + (y - x) = 14 - 4

→ 2y = 10

→ y = 5.

Putting This value in Equation (1) now,

→ x + 5 = 14

→ x = 9.

Hence, Our Required Two Digit Number is = 10x + y = 10*9 + 5 = 95. (Ans).

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Verification :-

→ 95 - 29 = 66. ( Both Digits Same.) .

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Answer 2

Answer:

95.

Step-by-step explanation:

Let us assume the number as (10x + y).

Sum = 14

x + y = 14

y = 14 - x -- equation (1).

given that, If we subtract 29 from the number then two digits are equal.

(10x + y) - 29 = (10z + z)

Substitute "y" value here,

10x + 14 - x -29 = 11z

9x - 15 = 11z

This (9x - 15) must be the multiple of 11. If the value of x is 9 it would be correct.

Hence substitute x value in equation (1).

y = 14 - x

y = 14 - 9

y = 5.

Hence , the number is (10x + y) = 10(9)+5 = 95.