In a meter bridge, the null point is found at a distance of 33.7 cm from terminal A (known resistance R is connected to the gap near to A). If the resistance of 12 Ω is connected parallel to unknown resistance X (which is connected to the gap near to terminal B), the null point is found at 51.9 cm. The value of X is 

CONCEPT: 

Meter bridge:

• The Meter Bridge is instruments based on the principle of the Wheatstone bridge and is used to measure an unknown resistance.
• In the case of a meter bridge, the resistance wire AC is 100 cm long. Varying the position of tapping point B, the bridge is balanced.
• If in the balanced position of bridge AB = l, BC (100 – l) so that

Also, 

EXPLANATION:

Given - Null point in 1^st case (l₁) = 33.7 cm, Null point in 2^nd case (l1) = 51.9 cm

• The null point in 1​st case (l1)

• When X is connected in parallel to R = 12 Ω, the resistance across the gap is R_eq 

• The null point in 2^nd case (l1)

Substitute  in the above equation, we get

⇒ X = 13.5 Ω