the product of 2 digit number is 1450.if the product of the tens place digit in thee numbers is 10 and the product of ones place digits in these numbers is 40 . find the numbers . please solve it step wise i need it very fast
Answers
Given : The product of two 2 digit numbers is 1450. If the product of the ten’s place digits in these numbers is 10 and the product of one’s place digits in these numbers is 40
To find : the numbers.
Solution:
Let say two numbers are
AB & CD
Value of AB = 10A + B
Value of CD = 10C + D
(10A + B)(10C + D) = 1450
=> 100AC + 10AD + 10BC + BD = 1450 Eq1
product of the ten’s place digits in these numbers is 10
=> AC = 10
Substitute in Eq 1
=> 100(10) + 10AD + 10BC + BD = 1450
=> 10AD + 10BC + BD = 450
Product of one’s place digits in these numbers is 40.
=> BD = 40
=> 10AD + 10BC + 40 = 450
=> 10AD + 10BC = 410
=> AD + BC = 41
AC = 10
BD = 40
AD + BC = 41
=> A(40/B) + B(10/A) = 41
=> 40A² + 10B² = 41AB
=> 40A² - 41AB + 10B² = 0
=> 40A² - 25AB - 16AB + 10B² = 0
=> 5A(8A - 5B) - 2B(8A - 5B) = 0
=> (5A - 2B) (8A - 5B) = 0
=> 5A - 2B = 0
=> A = 2 , B = 5 or A = 5 , B = 8
=> C = 5 , D = 8 or C = 2 , D = 5
AB = 25 CD = 58
or
AB = 58 CD = 25
Hence two numbers are 25 & 58
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