Question
When the sum of the squares of two positive integers is
given as 1,600, and their product is given as 768. Determine the value of the smaller integer.Solution
ATQ, Let, the two numbers be 'm' and 'n', such that, 'm > 'n'. ATQ, m 2 + n2 = 1600 And, m × n = 768 We know that, (a + b)2 = a2 + b2 + 2ab, and, (a - b)2 = a2 + b2- 2ab So, (m + n)2 = 1600 + 2 × 768 Or, (m + n)2 = 1600 + 1536 Or, (m + n)2 = 3136 Since both the numbers are greater than zero. So, m + n = 56 ....(i) Similarly, (m - n)2 = m2 + n2- 2mn So, m - n = 8 ....(ii) On subtracting equation (ii) from equation (i) , we get, 2n = 48 So, n = 24 So, the value of the smaller number = n = 24
Akshay invested Rs. 960 in two schemes P and Q in the respective ratio of 5:3. Scheme P and Q are offering simple interest at the rate of 7% per annum a...
The interest earned on investing Rs. 9000 for 2 years at the rate of 10% p.a., compounded annually, is used to purchase an article. If the article is la...
Mr. P invested Rs. ‘2x’ in scheme ‘A’ offering simple interest of 20% p.a. and reinvested the interest earned from scheme ‘A’ at the end of ...
A sum of Rs. 9,600 grows to Rs. 12,696 when invested at an annual compound interest rate of 'R%' for 2 years. What is the value of 'R'?
The difference between compound interest and simple interest at the same rate for Rs. 3600 for 2 years is Rs. 36. The rate of interest per annum is:
Roshan and Rahul received marks in their quarterly exam in a ratio of 9:8. Additionally, the ratio of marks Roshan obtained in the quarterly exam to the...
The interest received on investing Rs. (5p + 150) on simple interest at 15% p.a. for 2 years is Rs. (2p + 240). Find the ratio (p - 90):(p + 60)
Suresh earned an interest of Rs. 774 on principal amount of Rs. 2400 at some rate of compound interest in 2 years. How much more/less interest would he ...
A certain sum of money invested at R% p.a. fetches a compound interest (compounded annually) of 1560 and simple interest of Rs.1500 at the end of 2 year...
A man invested a certain amount of sum at 12.5% per annum simple interest and earned an interest of Rs.2100 after 3 years. If the same amount is investe...
Relevant for Exams:
