Question

Sunita cuts a sheet of paper into three pieces. Length of first piece is equal to the average of the three single digit odd prime numbers. Length of the second piece is equal to that of the first plus one-third the length of the third. The third piece is as long as the other two pieces together. The length of the original sheet of paper is
1. 13 units
2. 15 units
3. 16 units
4. 30 units

Answer 1

Correct Answer - Option 4 : 30 units

Given:

Length of the first piece = Average of three single-digit odd prime numbers

Length of the second piece = Length of first piece + 1/3 length of the third piece

Length of the third piece = Length of first piece + Length of the second piece

Calculation:

Let the three pieces be x, y and z

Length of x = Average of three single digit odd prime numbers

⇒  ( 3 + 5 + 7 ) / 3

⇒ 5

Length of y = x + (z/3)

y = ( 3x + z ) / 3

y = ( 15 + z ) / 3      ---(i)      (x = 5) 

z = x + y      ---(ii)

From (i) & (ii),

y = ( 15 + x + y ) / 3

3y = 15 + 5 + y

3y - y = 20

2y = 20 

y = 10

From (iii),

z = x + y

z = 10 + 5 

z = 15

Length of the original sheet = x + y + z 

⇒ 5 + 10 + 15 

⇒ 30 

∴ The length of the original paper is 30 units