Q: If the sum of two numbers is 55 and the H.C.F and L.C.M of these numbers are 5 and 120 respectively, then the sum of the reciprocals of the numbers is equal to
Solution: Let the numbers be a and b . Then, a+b =55 and ab = 5 x 120 = 600. Therefore, Required sum = 1a+1b=a+bab=55600=11120
Q: Three different containers contain 1365 litres, 1560 litres and 1755 litres of mixtures of milk and water respectively. What biggest measure that can measure all the different quantities exactly ?
Solution: From the given data, containers contain mixtures of milk and water as 1365 lit, 1560 lit and 1755 lit. Biggest measure that can measure all these different quantities exactly can be given by HCF of (1365, 1560, 1755) That can be found as HCF of 1365, 1755 = 195 Now, HCF of 195 and 1560 = 195 Hence, biggest measure that can measure all the given different quantities exactly is 195 lit.
Q: A natural number, when divided by 9, 10, 12 or 15, leaves a remainder of 3 in each case. What is the smallest of all such numbers?
Solution: LCM of 9,10,12,15 is 180Smallest natural number to get remainder of 3 is (180 + 3) = 183
Q: The HCF of two numbers is 11 and their LCM is 330. If one of the number is 55. Find the other number.
Solution: 66
Q: Mr. Devesh borrowed Rs.4,500 at 4% per annum compound interest. The compound interest compounded annually for 2years is
Solution: Rs. 367.2
Q: Shams invested Rs. 5000 at 10% per annum compound interest. After n years, Shams received Rs. 1655 more. Find the value of n.
Solution: 3 years
Q: The population of a town was 3600 three years back. It is 4800 right now. What will be the population three years down the line, if the rate of growth of population has been constant over the years and has been compounding annually?
Solution: The population grew from 3600 to 4800 in 3 years. That is a growth of 1200 on 3600 during three year span. Therefore, the rate of growth for three years has been constant. The rate of growth during the next three years will also be the same. Therefore, the population will grow from 4800 by 4800*13= 1600 Hence, the population three years from now will be 4800 + 1600 = 6400
Q: Rs.100 doubled in 5 years when compounded annually. How many more years will it take to get another Rs.200 compound interest
Solution: Rs.100 invested in compound interest becomes Rs.200 in 5 years. The amount will double again in another 5 years. i.e., the amount will become Rs.400 in another 5 years. So, to earn another Rs.200 interest, it will take another 5 years.
Q: The average temperature of the town in the first four days of a month was 58 degrees. The average for the second, third, fourth and fifth days was 60 degrees. If the temperatures of the first and fifth days were in the ratio 7 : 8, then what is the temperature on the fifth day ?
Solution: Sum of temperatures on 1st, 2nd, 3rd and 4th days = (58 * 4) = 232 degrees ... (1) Sum of temperatures on 2nd, 3rd, 4th and 5th days - (60 * 4) = 240 degrees ....(2) Subtracting (1) From (2), we get : Temp, on 5th day - Temp on 1st day = 8 degrees. Let the temperatures on 1st and 5th days be 7x and 8x degrees respectively. Then, 8x - 7x = 8 or x = 8. Temperature on the 5th day = 8x = 64 degrees.
Q: The captain of a cricket team of 11 members is 26 years old and the wicket keeper is 3 years older. If the ages of these two are excluded, the average age of the remaining players is one year less than the average age of the whole team. What is the average age of the team ?
Solution: Let the average age of the whole team be x years. 11x - (26 + 29) = 9 (x - 1) => 11x - 9x = 46 => 2x = 46 => x = 23. So, average age of the team is 23 years.
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