Quantity 1:

Let the sum be RS. 100. Then,

⇒ S.I. for first six MONTHS = [(100 × 10 × 1)/100 × 2] = Rs. 5

⇒ S.I. for NEXT six months = [(105 × 10 × 1)/100 × 2] = Rs. 5.25

⇒ So, amount at the end of 1 YEAR = Rs. (100 + 5 + 5.25) = Rs. 110.25

⇒ EFFECTIVE rate = (110.25 – 100) = 10.25%

Quantity 2:

let the original rate be r%

Then the new rate will be 2r%

⇒ (725 × r × 1)/100 + (362.50 × 2r × 1)/100 × 3 = 33.50

⇒ (2175 + 725) r = 33.50 × 100 × 3 = 10050

⇒ r = 10050/2900 = 3.46%

⇒ Original rate = 3.46%

Quantity 3:

Let the interest be r%

Difference between SI – CI

⇒ [15000 × (1 + r/100)² – 15000] – [15000 × r × 2/100] = 96

⇒15000 × [(1 + r/100)² – 1 – (r × 2/100)] = 96

⇒ 15000 × [(r + 100)² – 10000 – 200 r)/10000] = 96

⇒ r² = 96 × 2/3 = 64

⇒ r = 8%

Comparing all three quantities

∴ Quantity 1 > Quantity 3 > Quantity 2