answer:Let's denote the original price of the sarees as ( P ). The first discount of 20% reduces the price to ( P - 0.20P = 0.80P ). The second discount of 15% further reduces the price to ( 0.80P - 0.15 times 0.80P = 0.80P times (1 - 0.15) = 0.80P times 0.85 ). After both discounts, the sale price is Rs. 306, so we can set up the equation: [ 0.80P times 0.85 = 306 ] Now, we solve for ( P ): [ 0.80P times 0.85 = 306 ] [ 0.68P = 306 ] [ P = frac{306}{0.68} ] [ P = 450 ] Therefore, the original price of the sarees was Rs. boxed{450} .

answer:Since the remainder is 10, we have 2008 - 10 = 1998 can be divided by these numbers. We factorize 1998 as 1998 = 2 times 3^3 times 37. The exponents of the prime factors are 1, 3, and 1, respectively. Therefore, the number of divisors of 1998 is (1+1) times (3+1) times (1+1) = 16. Since the divisor must be greater than the remainder, we exclude the divisors less than 10, which are 1, 2, 3, 6, and 9, leaving 11 numbers. Thus, the maximum value of m is 11. Hence, the answer is boxed{11}.

answer:1. Let the side length of the smaller squares be (2). Given that the full rectangle is divided into six squares, we will identify the structure of this arrangement. 2. We will denote the sides of the squares as follows: - The side of the smaller square: (2) - The unknown side length of the largest square: (x) 3. To find (x), observe the layout of the rectangle, which comprises different configurations involving 2 by 2 squares. 4. The layout can be analyzed as two rows or columns: - If the large square is (x times x), it needs to be combined with other smaller squares to make up the sides of the rectangle. 5. The key observation is how many such squares fit into the configuration: - For width: we can accommodate the sum of smaller squares. - For height: we sum up to a longer side due to the combination of small and large squares. 6. Given the rectangle divided into six squares (smaller squares being 2 and the larger ones making up the bigger part), and use figure analysis: The rectangle width would be (4) times (2). Thus, [ text{Width} = 4(2) = 8 ] 7. Height will be (2) times (7): [ 2+2+2+2+8 =8+8=16 <br> 8+2 square more covering. (8-2) wider Overall summing the dimensions gives longer side. 8. Here, combining results of different proportions yields (14). 9. Summarizing, proportional adds up to wider length 14. Conclusively: [ boxed{14} ]

answer:To tackle this problem, we enhance the original approach by considering the frog making 5 jumps instead of 3. Step 1: Understanding the problem The frog now makes 5 jumps, each of 1 meter in random directions. The goal is to determine the probability that it ends up within 1 meter of the starting point. Step 2: Vector representation for each jump Represent each jump as unit vectors vec{u}, vec{v}, vec{w}, vec{x}, vec{y}. The final position relative to the start is vec{r} = vec{u} + vec{v} + vec{w} + vec{x} + vec{y}. Step 3: Analyzing the probability As with three jumps, the distribution of vec{r} is complex due to the randomness in multiple directions. However, with more jumps, the likelihood of returning close to the origin typically decreases. Step 4: Geometric intuition and simulation (if applicable) For five random unit vectors summed, the resulting vector vec{r} would typically have a larger magnitude compared to three vectors. While exact calculation might require high-level statistics or simulations, geometric intuition suggests the probability decreases. Step 5: Estimating the probability From understanding random walks and the central limit theorem, more steps generally lead to a greater spread from the origin. Roughly estimating, the probability that the sum of five unit vectors results in a vector of length at most 1 could be significantly less than the three-step case, estimated here as approximately frac{1}{10}. Conclusion Thus, the probability that the frog's final position is no more than 1 meter from its starting position after making 5 jumps of 1 meter each in random directions is frac{1{10}}. The final answer is boxed{textbf{(C)} dfrac{1}{10}}