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  1. LPU MCA Semester 1
  2. PEA515
  3. Unit 4

PEA515 · Unit 4: Ratio, proportion and mixtures

Problems on ages and partnership

30 practice questions · in the ETE syllabus

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Key points

  • Ages move together; the difference stays fixed
  • Ratio of ages gives ages as multiples of k
  • Partnership profit shares follow capital x time
  • A late joiner counts only for the remaining months

Ages problems are solved by letting one age be a variable and turning each statement into an equation. Keep three rules in mind: ages increase by the same number of years for everyone, the difference between two ages never changes, and ages in the past are found by subtracting.

SituationSetup
Ratio a : b and sum SAges are ak and bk with k = S / (a + b)
Father is x times the son; after n years y timesx s + n = y (s + n)
Ratio p : q n years ago, sum S nowPast sum = S - 2n, so past ages are pk and qk; add n back

In a partnership profit is shared in the ratio of capital x time. If A invests X for m months and B invests Y for n months, the ratio is Xm : Yn. A partner who joins later is counted only for the months remaining: B joining after 4 months in a 12-month year is counted for 8 months.

Example: A puts 2000 for 12 months and B puts 10000 for 5 months, so the ratio is 24000 : 50000 = 12 : 25. A profit of 6660 gives B 6660 x 25 / 37 = 4500.

Exam trap: sharing in the ratio of capital alone ignores the time each partner's money was invested.

Try two questions

Question 1 · Tier 4, Analyse

A father is 4 times as old as his son. After 14 years the father will be 2 times as old as his son. What is the son's present age (years)?

  1. 7
  2. 28
  3. 21
  4. 14
Show the answer

A. Let the son's age be s: 4s + 14 = 2(s + 14), which gives s = 7.

Why not B: Gives the father's age instead of the son's.

Why not C: Gives the son's age after the given years.

Why not D: Reports the number of years.

Question 2 · Tier 2, Understand

Two brothers have a combined age of 99 years. 7 years ago the ratio of the elder's age to the younger's was 9 : 8. How old is the elder now?

  1. 47
  2. 45
  3. 52.41
  4. 52
Show the answer

D. 7 years ago the sum was 85, so one part is 5. The elder was 45, so he is now 52.

Why not A: Gives the younger person's age.

Why not B: Gives the elder's age n years ago.

Why not C: Splits the present sum in the ratio of the past ages.