Question

c) 1,000
18) The sum of 2 digit of a number is 15 If 9 is added to the number, the
resulting number is equal to the original number with the digits
Interchanged the numbers.
किसी संख्या के दो अंकों का योग 15 है।यदि उस संख्या में आ जोड़ दिया
जाए तो संख्या के अंक पलट जाते हैं। संख्या बताओ।
a)78
b) 38
c) 42
d) none of these​

Answer 1

Step-by-step explanation:

According to first condition

x+y=15----------(1)

According to second condition

10x+y+9=10y+x

10x+y+9-10y-x=0

9x-9y=-9

x-y=-1-----------(2)

from (1)and(2) we get

x+y=15

x-y= -1

______

2x=14

x=7 and y=8

so the number is 78

verification

78+9=87

Answer 2

Given:-

• The sum of 2 digits of a number is 15.

• If 9 is added to the number, the resulting number is equal to the original number with the digits Interchanged.

To Find:-

• Find the two digit number.

Concept:-

• Let's go through the concept first. Form two equations firstly according to the conditions mentioned in the question and substitute the values,equate them and solve it.

Solution:-

Let the two digits of the number be x(ten's place) and y(one's place)

The two digit number = 10x + y

Sum of two digits of a number = 15

According to the question we have!

⟹ x + y = 15

⟹ x = 15 - y______(1)

If 9 added to the number,then the digits are reversed

⟹ 10x + y + 9 = 10y + x

⟹ 10x - x + y - 10y = - 9

⟹ 9x - 9y = - 9

⟹ x - y = - 1______(2)

Substituting the value of x from (1) to (2) we get,

⟹ x - y = - 1

⟹ 15 - y - y = - 1

⟹ -2y = - 1 - 15

⟹ - 2y = - 16

⟹ - y = - 16/2

⟹ - y = - 8

⟹ y = 8

Hence,

The value of y is 8.

Now,substitute value of y in any eq to find the value of x.

⟹ x = 15 - y

⟹ x = 15 - 8

⟹ x = 7

Hence,

The value of x is 7

Therefore,

The ten's place digit is 7 and the one's place digit is 8.So,The two digit number is 78.

Verification:-

The number we first took was 10x + y

⟹ 10x + y = 15

⟹ 10 × 7 + 8 = 15

⟹ 78 = 15

⟹ 7 + 8 = 15

The sum of two digits of a number is 15.Hence,it is correct.

When 9 is added,the digits interchange its place.

⟹ 78

⟹ 78 + 9 = 87

The digits are interchanged.Hence,it is correct.

Therefore,

It is verified.

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