Question

A x 4 = E
B ÷ 4 = E
C + 4 = E
D - 4  = E
___________
& A + B + C + D = 100

*what is the value of E ?*​

Answer 1

Given

→ A × 4 = E

→ B ÷ 4 = E

→ C + 4 = E

→ D - 4 = E

Also, A + B + C + D = 100

To find

Value of E

Solution

→ A × 4 = E

→ A = E/4 ............(1)

→ B ÷ 4 = E

→ B = 4E ..............(2)

→ C + 4 = E

→ C = E - 4 ............(3)

→ D - 4 = E

→ D = E + 4 ............(4)

Now,

A + B + C + D = 100

Substitute value of A, B, C and D above

→ (E/4) + (4E) + (E - 4) + (E + 4) = 100

Take L.C.M. i.e. 4

→ [E + 16E + 4(E - 4) + 4(E + 4)]/4 = 100

Solve the brackets

→ (E + 16E + 4E - 16 + 4E + 16)/4 = 100

Now, add and subtract the values given in bracket

→ (25E)/4 = 100

Multiply with 4 on both sides

→ (25E)/4 × 4 = 100 × 4

→ 25E = 400

→ E = 400/25

→ E = 16

Therefore, the value of E is 16.

Answer 2

Answer:-

• A × 4 = E

➜ A = E/4 .....(1)

• B ÷ 4 = E

➜ B = E × 4 .......(2)

• C + 4 = E

➜ C = E - 4 ......(3)

• D - 4 = E

➜ D = E + 4 ......(4)

Using (1),(2),(3) and (4),

• A + B + C + D = 100

➜ E/4 + 4E + E-4 + E+4 = 100

➜ E/4 + 4E + E + E= 100

➜ E/4 + 4E + 2E= 100

➜ E/4 + 6E= 100

Taking LCM,

➜ (E + 24E)/4 = 100

➜ 25E/4 = 100

➜ 25E = 100 × 4

➜ 25E = 400

➜ E = 400/25

➜ E = 16

$\rule{200}2$