Question
The cube of the difference between two given natural
numbers is 1728, while the product of these two given numbers is 108. Find the positive difference between the cubes of these two given numbers.Solution
1st natural number = x 2nd natural number = y (x - y)3 = 1728 (x - y) = 3√1728 = 12           … (1) squaring both sides  (x - y) ² = 144 x2+y2-2xy =144 x² + y² = 144 + 216 = 360 Now, (x + y) = √ (x² + y² + 2xy) =√ (360 + 216) = √576 = 24  … (2) Now Eq (1) + Eq (2). x-y+x+y =12+24=36 2x =36 x=18 y=6 Now positive difference between the cubes= (18)3-(6)3 =5832-216 =5616.
Rs. (X+500) is invested in scheme A for 5 years at 10 % simple interest. The received amount is then invested in another scheme B offering 10% interest ...
A sum of money doubles itself in 5 years at simple interest. What is the rate of interest per annum?
A sum of money amounts to ₹8700 in 2 years at a simple interest rate of 8% per annum. If the same sum is invested at compound interest with the same r...
A certain sum of money becomes 6000 in 6 years and Rs. 6240 in 10 years at any certain rate of simple interest. Find the principal amount.
A certain sum of money becomes 5 times of itself in 25 years at simple interest. In how many years does it become double of itself at the same rate of s...
Rs. ’P’ invested at a rate of 15% p.a. compound interest (compounded annually) amounts to Rs. 8464 at the end of 2 years. Find the simple interest e...
Atul has Rs.200 with him. He invested 40% of the amount at 5% p.a. for 6 years and rest at 20% p.a. for 5 years. Find the sum of simple interests receiv...
A certain sum of money amounts to Rs 1331 in 3 years at 10 percent compounded annually. Find the value of (CI-SI)?
Rs. 25,000 invested at simple interest of 6% p.a. yields the same interest after 2 years as Rs. 40,000 when invested at simple interest of 'y%' p.a. yie...
Rs.7800 is divided into two parts such that if one part be invested at 3% and the other at 5%, the annual interest from both the investments is Rs. 320....
Relevant for Exams:
