Math, asked by MeenaHandique, 11 months ago

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

Answered by amitnrw
6

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

Answered by ajoygogoi64
0

Answer:

Sort formed please

Similar questions