Let principal be P.

Acc to ques.: P∗4∗13100∗12 – P∗6∗8100∗12 = 40

P(521200 - 481200) = 40

P = Rs. 12000.

for calculating the compound interest at 15% apply 15+15+15*15/100 for two years equal to 32.25 I.e. 2.25% extra from 30% of simple interest 2.25%of 20000=450

MP=400

D%=10

So, SP=400*90/100=360

P%=12

CP=360*100/(100+12)=300

LCM = 2970; HCF = 30

Factors of LCM = 2x3x3x3x5x11 and of HCF = 2x3x5

Product of two numbers = Product of LCM and HCF of the numbers

= 2x3x3x3x5x11x2x3x5

a = 2; b2 – ab = - 1

b2 – 2b + 1 = 0 (given a = 2)

(b - 1)2 = 0

b = 1

log_(a+b)(a3+b3) = ?

Put values: log₍₁₊₂₎(13+23) = log3(1+8) = log3(9) = log3(32) = 2log3(3) = 2

Alternatively;

a3+b3 = (a+b)(a2+b2-ab)

log_(a+b)(a+b)(a2+b2-ab) = log(a+b)_(a+b) + log_(a+b)(a2+b2-ab)

= 1 + log(3)(4 - 1) = 1 + 1 = 2