ABCDE is a five digit number. Two six digit numbers are formed by putting 9 to the left and right of it respectively. If the former is equal to 4 times of the latter, find a+b+c+d+e.
Answers
Answer:
ABCDE = 23076
a+b+c+d+e = 18
Step-by-step explanation:
ABCDE is a five digit number. Two six digit numbers are formed by putting 9 to the left and right of it respectively. If the former is equal to 4 times of the latter, find a+b+c+d+e.
5 Digit number = ABCDE
6 Digit number = 9ABCDE & ABCDE9
9ABCDE = 4 * ABCDE9
=> 9 * 10⁵ + A* 10⁴ + B* 10³ + C* 10² + D* 10¹ + E = 4 * (A * 10⁵ + B* 10⁴ + C* 10³ + D* 10² + E* 10¹ + 9)
=> 9 * 10⁵ + A* 10⁴ + B* 10³ + C* 10² + D* 10¹ + E = 4A * 10⁵ +4B* 10⁴ + 4C* 10³ + 4D* 10² + 4E* 10¹ + 36
=>9 * 10⁵ + A* 10⁴ + B* 10³ + C* 10² + D* 10¹ + E = 4A * 10⁵ +4B* 10⁴ + 4C* 10³ + 4D* 10² + 4E* 10¹ + 30 + 6
=> 9 * 10⁵ + A* 10⁴ + B* 10³ + C* 10² + D* 10¹ + E = 4A * 10⁵ +4B* 10⁴ + 4C* 10³ + 4D* 10² + (4E+3)* 10¹ + 6
Hence E = 6 putting Vale of E = 6
=> 9 * 10⁵ + A* 10⁴ + B* 10³ + C* 10² + D* 10¹ + 6 = 4A * 10⁵ +4B* 10⁴ + 4C* 10³ + 4D* 10² + (4*6+3)* 10¹ + 6
=> 9 * 10⁵ + A* 10⁴ + B* 10³ + C* 10² + D* 10¹ + 6 = 4A * 10⁵ +4B* 10⁴ + 4C* 10³ + 4D* 10² + (27)* 10¹ + 6
=> 9 * 10⁵ + A* 10⁴ + B* 10³ + C* 10² + D* 10¹ + 6 = 4A * 10⁵ +4B* 10⁴ + 4C* 10³ + 4D* 10² + (20 + 7)* 10¹ + 6
=> 9 * 10⁵ + A* 10⁴ + B* 10³ + C* 10² + D* 10¹ + 6 = 4A * 10⁵ +4B* 10⁴ + 4C* 10³ + (4D+2)* 10² + 7* 10¹ + 6
=> D = 7 putting Vale of D = 7
=> 9 * 10⁵ + A* 10⁴ + B* 10³ + C* 10² + 7* 10¹ + 6 = 4A * 10⁵ +4B* 10⁴ + 4C* 10³ + (4*7+2)* 10² + 7* 10¹ + 6
=> 9 * 10⁵ + A* 10⁴ + B* 10³ + C* 10² + 7* 10¹ + 6 = 4A * 10⁵ +4B* 10⁴ + 4C* 10³ + (30)* 10² + 7* 10¹ + 6
=> 9 * 10⁵ + A* 10⁴ + B* 10³ + C* 10² + 7* 10¹ + 6 = 4A * 10⁵ +4B* 10⁴ + (4C+3)* 10³ + (0)* 10² + 7* 10¹ + 6
=> C = 0 putting Vale of C = 0
=> 9 * 10⁵ + A* 10⁴ + B* 10³ + 0* 10² + 7* 10¹ + 6 = 4A * 10⁵ +4B* 10⁴ + (4*0+3)* 10³ + (0)* 10² + 7* 10¹ + 6
=> 9 * 10⁵ + A* 10⁴ + B* 10³ + 0* 10² + 7* 10¹ + 6 = 4A * 10⁵ +4B* 10⁴ + (3)* 10³ + (0)* 10² + 7* 10¹ + 6
=> B = 3 putting Vale of B = 3
=> 9 * 10⁵ + A* 10⁴ + 3* 10³ + 0* 10² + 7* 10¹ + 6 = 4A * 10⁵ +(4*3)* 10⁴ + (3)* 10³ + (0)* 10² + 7* 10¹ + 6
=> 9 * 10⁵ + A* 10⁴ + 3* 10³ + 0* 10² + 7* 10¹ + 6 = 4A * 10⁵ +(10+2)* 10⁴ + (3)* 10³ + (0)* 10² + 7* 10¹ + 6
=> 9 * 10⁵ + A* 10⁴ + 3* 10³ + 0* 10² + 7* 10¹ + 6 = (4A+1) * 10⁵ +(2)* 10⁴ + (3)* 10³ + (0)* 10² + 7* 10¹ + 6
=> A =2 also 4A + 1 = 9 is being satisfied
A + B + C + D + E = 2 + 3 + 0 + 7 + 6 = 18
ABCDE = 23076
923076 = 4*230769
Answer:
Sort formed please