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WAEC 2024 · Paper 2 · Q10

  1. (a)

    In a man’s will, he gave 25\frac25 of the total acres of his farm to his wife and 13\frac13 of what was left to the family. The rest of the farm was to be shared amongst his three children in the ratio 3:5:23 : 5 : 2. Given that the child with the least share received 8 acres, calculate the: (i) total acres the man left; (ii) number of acres the wife received.

    Separate values with commas, e.g. 3, −2

  2. (b)

    The price of a television set is $1,600.00. It can be bought by paying a deposit of $400.00 and the rest in 12 monthly instalments at 25%25\% per annum simple interest. If the set is bought by instalment, find the total cost ($).

Worked solution (try it first)

(a)

  1. Let the total be TT acres.
  2. The wife gets 25T\frac25T, leaving 35T\frac35T.
  3. The family gets 13\frac13 of that, 15T\frac15T.
  4. The children get the rest: T−25T−15T=25TT - \frac25T - \frac15T = \frac25T.
  5. The children share in the ratio 3:5:23 : 5 : 2 (10 parts).
  6. The smallest share (2 parts) is 8 acres, so one part is 4 acres and the children have 10×4=4010 \times 4 = 40 acres.

(i)

  1. 25T=40\frac25T = 40, so T=100T = 100 acres.

(ii)

  1. The wife received 25×100=40\frac25 \times 100 = 40 acres.

(b)

  1. Balance after the deposit: 1600−400=12001600 - 400 = 1200 dollars.
  2. Interest for 12 months (1 year) at 25%25\%: 0.25×1200=3000.25 \times 1200 = 300 dollars.
  3. Total cost =400+1200+300=1900= 400 + 1200 + 300 = 1900, that is $1,900.

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