The product (a + b) (a - b) (a² - ab + b²) (a² + ab + b²) is equal to:
a⁶ - b⁶
The expression simplifies to a⁶ - b⁶ using the identity for the product of differences and sums of squares. Therefore, the correct answer is a⁶ - b⁶.
Important Questions from Partnership
Three partners X, Y and Z started their business by investing ₹40,000, ₹38,000 and ₹30,000, respectively. After 6 months, X and Z made additional investments of ₹20,000 and ₹15,000 respectively, whereas Y withdrew ₹8,000. Find the share of Y (in ₹) in the total profit of ₹38,880 made at the end of the year.
A, B and C invested their capitals in the ratio 2 ∶ 3 ∶ 5. The ratio of months for which they invested is 4 ∶ 2 ∶ 3, respectively. If the difference between the profit shares of A and B is Rs. 1,86,000, then C's share of profit (in Rs.) is:
A started a business with a capital of Rs. 54,000 and admitted B and C after 4 months and 6 months, respectively. At the end of the year, the profit was divided among the three in the ratio 1 ∶ 4 ∶ 5. What is the sum (in Rs.) of the capitals invested by B and C?
A, B and C started a business in partnership. Initially, A invested Rs. 29,000, while B and C invested Rs. 25,000 each. After 4 months, A withdrew Rs. 3,000. After 2 more months, C invested Rs. 12,000 more. Find the share of C( in Rs.) in the profit of Rs. 33,200 at the end of the year.
A, B and C invest in a business in the ratio 4 ∶ 5 ∶ 7. C is a sleeping partner, so his share of profits will be half of what it would have been if he were a working partner. If they make Rs 36,000 profit of which 25% is reinvested in the business, how much does B get (in Rs)?
