A person bought 60 quintals of rice of two different sorts for Rs. 4642·50. The better sort costs Rs. 80 per quintal and the worse Rs. 75·50 per quintal. How many quintals were there of each sort?

? = 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