The 1st term of an HP is 1/17 and the product of the 2nd and 4th term equals to the products of 5th and 6th term of the HP. Find the 3rd term of the HP.?

? = 198.995 x 12.005 + 16.24 x 6.95
= 199 x 12 +16 x 7 = 2388 + 112 = 2500

The face value of 8 in 458926 is 8

Each of the number except 28, is a multiple of 3.

6674 x 625 = 6674 x (5)⁴
= 6674 x (10⁴/2⁴
= 66740000/16 = 4171250

As we know that given in question,
ax + by = 6 ........................ (i)
bx ? ay = 2 ........................ (ii)
On squaring the both equation and adding,
a² x² + b² y² + 2abxy + b² x² + a² y² ? 2abxy = 36 + 4
? x² (a² + b²) + y² (a² + b²) = 40
? (a² + b²) (x² + y²) = 40
As per given question, x² + y² = 40 , Put this value in above equation, we will get
? (a² + b²) × 4 = 40
? a² + b² = 10

Clearly, n (S) = 52, there are 4 kings and 4 queens
? P(E) = n (E) / n (S) = 8/52 = 2/13

Lat the 4th proportional = N
Then, 4 : 16 : : 7 : N
? 4/16 = 7/N
? 4N = 7 x 16
? N = (7 x 16)/4 = 7 x 4 = 28

CP = 100/70 = x 6384 = ? 9120
To gain 30%, SP = 130% of 9120
SP = (130/100) x 9120 = ? 11856

(2/3) x (6/8) x (2/3) x (3/4) = 1/4 = 0.25

Second number = (LCM x HCF) / first number
= (72 x 12)/ 24 = 36
Difference between the two numbers
= 36 - 24 = 12