BANK & INSURANCE (SIMPLIFICATION SURDS & INDICES)

0.64 = 0.8²  (because 0.8 × 0.8 = 0.64)

0.512 = 0.8³ (because 0.8³ = 0.512)

(0.64)⁷⁸ = (0.8²)⁷⁸ = 0.8^(156)

(0.512)³⁹ = (0.8³)³⁹ = 0.8^(117)

So, (0.64)⁷⁸ ÷ (0.512)³⁹ = 0.8^(156−117) = 0.8^39

Hence, ? = 39

Answer: 39

1560 ÷ 12 = 130

4004 ÷ 13 = 308

So, 130 − 308 = −178

−178 = ?² − 322

?² = −178 + 322 = 144

? = √144 = 12

Answer: 12

55% of 800 = 440

33×4 = 132

396 ÷ 18 = 22

LHS = 440 + 132 − 22 = 550

(?)² − 26 = 550 ⇒ (?)² = 576 ⇒ ? = 24

Answer: 24

3⁴ = 81 and 3×3² = 3×9 = 27 ⇒ 81 ÷ 27 = 3

12² = 144 and 4×2 = 8 ⇒ 144 ÷ 8 = 18

Total = 3 + 18 = 21

Answer: 21

√2116 = 46

2³% = 8%

8% of 2700 = 216

46 − 216 + 180 = 10

Answer: 10

√8×√8 = 8 ⇒ (8)² = 64

√9 = 3

LHS = 64 + 3 = 67

(?)³ + 3 = 67 ⇒ (?)³ = 64 ⇒ ? = 4

Answer: 4

450 ÷ 15 = 30

208 ÷ 8 = 26

LHS = 30 + 26 − 16 = 40

?² − 41 = 40 ⇒ ?² = 81 ⇒ ? = 9

Answer: 9

√225 = 15

248 ÷ 8 = 31

RHS = 31 + 929 = 960

4^x × 15 = 960 ⇒ 4^x = 64

64 = 4³ ⇒ x = 3

Answer: 3

30% of 580 = 174

60% of 700 = 420

LHS = 174 + 420 = 594

√4225 = 65

?² = 594 − 65 = 529

? = √529 = 23

Answer: 23

32.001 ≈ 32, 5.05² ≈ 25, 4.01 ≈ 4

First bracket ≈ (32×25)/4 = 200

√2499 ≈ 50

10.24% of 50 = 0.1024×50 = 5.12

Product ≈ 200×5.12 = 1024 = 2¹⁰

So, x = 10

Answer: 10