Current I1 = (2E)/(2r + R)
Heat in situation 1 ⇒ J1 = I1²Rt ⇒ J1 = ((2E)/(2r + R))²Rt
Similarly I2 = (E/((r/2) + R))
Heat in situation 2 ⇒ J2 = I2²Rt ⇒ J2 = (E/((r/2) + R))²Rt
⇒ J1 = 2.25J2 (Given)
((2E)/(2r + R))² = 9/4 × (E/((r/2) + R))²
4(r + 2R)² = 9(2r + R)²
2(r + 2R) = 3(2r + R)
2r + 4R = 6r + 3R
R = 4r = 4Ω