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WAEC 2012 · Paper 2 · Q6

  1. (a)

    A boy had MM dalasis (D). He spent D15 and shared the remainder equally with his sister. If the sister's share was equal to 13\frac13 of MM, find the value of MM.

  2. (b)

    A number of tourists were interviewed on their choice of means of travel. Two-thirds said that they travelled by road, 1330\frac{13}{30} by air and 415\frac{4}{15} by both air and road. If 20 tourists did not travel by either air or road, (i) represent the information on a Venn diagram; (ii) how many tourists: (A) were interviewed; (B) travelled by air only?

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

Worked solution (try it first)

(a)

  1. After spending D15 the boy had M−15M - 15.
  2. He shared it equally, so his sister got M−152\frac{M - 15}{2}.
  3. This equals 13\frac13 of MM: M−152=M3\frac{M - 15}{2} = \frac{M}{3}.
  4. Multiply both sides by 6: 3(M−15)=2M3(M - 15) = 2M.
  5. So 3M−45=2M3M - 45 = 2M and M=45M = 45.

(b)

  1. Let the number of tourists be xx.
  2. Road only =23x−415x=615x= \frac23x - \frac4{15}x = \frac{6}{15}x.
  3. Air only =1330x−415x= \frac{13}{30}x - \frac4{15}x
    =530x= \frac{5}{30}x
    =16x= \frac16x.
  4. Both =415x= \frac4{15}x, and neither =20= 20.
  5. The four regions of the Venn diagram make up everyone: 615x+16x+415x+20=x\frac{6}{15}x + \frac16x + \frac4{15}x + 20 = x.
  6. With denominator 30: 12+5+830x+20=x\frac{12 + 5 + 8}{30}x + 20 = x, so 2530x+20=x\frac{25}{30}x + 20 = x.
  7. Then 530x=20\frac{5}{30}x = 20 and x=120x = 120 tourists.
  8. Air only =16×120=20= \frac16 \times 120 = 20 tourists.

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