Math, asked by MdAli7072, 1 year ago

two digit number is such that the product of its digits is 16when 54 is subtracted from the number,the digits interchange their places.find the number.

Answers

Answered by anurajpikeovx7wt
0
let the digits of a number be x and y where x is ten's digit
so number= 10x+y---(i)
reverse of the number = 10y+x....(ii)
Given
(i)-54=(ii)
10x+y-54=10y+x
9x-9y=54
x-y=6....(3)

Given xy=16
so y=16/x....(4)

from 3 and 4 we get
x-16/x=6
x∧2-16=6x
x∧2-6x-16=0
x∧2-8x+2x-16=0
(x-8)(x+2)=0
x=8 since x=-2 isn't possible
so y=2
number =82


Verify
82-54=28

anurajpikeovx7wt: Shortcut method maybe
anurajpikeovx7wt: 16=2*8,4*4 possible numbers=28,44,82 and since 54 is being subtracted so number is >54 which only leaves 82
anurajpikeovx7wt: this shortcut method can't be used in school exams only for competitive MCQ exams where you need to save time
Answered by mathsdude85
0

SOLUTION:

Let the two digit number be 10x + y

Given : product of its digits(xy) = 16

xy = 16...................(1)

When 54 is subtracted from the number, the digits interchange their places

10x + y - 54  = 10y + x

10x + y - 10y - x = 54

9x - 9y = 54

9(x - y) = 54

x - y = 54/9

x - y = 6

x = 6 + y……………….(2)

Put this value of x in eq 1.

xy = 16

(6 + y)y = 16

6y + y² = 16

y²  + 6y - 16 = 0

y² +  8y - 2y - 16 = 0

[By middle term splitting]

y(y + 8) - 2(y + 8) = 0

(y - 2 ) ( y + 8) = 0

(y - 2 ) = 0   or ( y + 8) = 0

y = 2  or y = - 8

Since, a digit can't be negative, so y ≠ - 8.

Therefore , y = 2

Put this value of y in eq 1,

xy =16

x× 2 = 16

x = 16/2 = 8

x = 8

Required number = 10x + y  

= 10(8) + 2

= 80 + 2

Required number = 82

Hence, the Required two digit number is 82.

HOPE THIS ANSWER WILL HELP YOU...

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