Question
A farmer wants to divide Rs 1,22,000 between his sons ,
who are 18 and 20 years old respectively, in such a way that the sum divided at the rate of 20% per annum, compounded annually, will give the same amount to each of them when they attain the age of 22 years. How should he divide the sum?Solution
Let the farmer give Rs x to the 18 years old son and the remaining Rs (1,22,000 - x) to his 20 years old son. Now, [x(1+(20/100))]4 = (1,22,000 - x) (1+(20/100))2 ⇒ [x(120/100)]2 = (1,22,000 - x)  ⇒ [x(6/5)]2 = (1,22,000 - x)  ⇒ x(36/25) = (1,22,000 - x) ⇒ ((36/25)+1) x = 1,22,000 ⇒ ((36 + 25)/25) x = 1,22,000 ⇒ x = (1,22,000 × 25)/61 = 50,000 ∴ x = Rs 50,000 For 18 years old son = Rs 50,000 For 20 years old son = Rs 72,000 Alternate shortcut method: They will get the sum in 2nd to 1st child in the ratio of = (1+R/100)(difference between their age) = (1+(20/100))(20-18) = (6/5)2 = 36/25 So for 18 years old(1st child) , sum = [25/(36+25)] × 122000 = (25/61) × 122000 = 50000 & for 20 years old(2nd child) , sum = [36/(36+25)] × 122000 = (36/61) × 122000 = 72000
Average marks scored by each boy in a class were 80, whereas that by each girl were 88. If the number of boys is 50% more than the number of girls, then...
The average of 27 numbers is 20.The average of first 13 numbers is 15 and that of the last 13 numbers is 18. What will be the 27th number?
Average age of a class of 25 students is 13 years. Average age of the class is increased by 30 months if the age of the teacher is included. Find the ag...
The average of two consecutive even numbers is 69. If the smaller number is increased by 10% and the larger number is decreased by 10%, then find the di...
In an exam, the average score of 300 students is 48. If the average score of the students who passed is 60, and the average score of those who failed is...
The average weight of 25 employees in an office increases by 0.8 kg when the weight of the manager is included. If earlier the average weight of the emp...
- The average of 9 scores is 45. If two new scores are added and their average is 'x', the overall average becomes 20% more than the previous average. Find t...
In an Aerobic class, the average age of all the members was 54.5 years, 11 members left the class and 7 new members joined. If the average age increased...
The batting average for 27 innings of a cricket player is 47 runs. His highest score in an innings exceeds his lowest score by 157 runs. If these two i...
Average weight of all the people in a group is 55 kg. When two people of weight 63 kg and 77 kg left the group, average weight reduces by 1.5 kg. Find t...
Relevant for Exams:
