Sonny is twice as old as Wale. Four years ago, he was four times as old as Wale. When will the sum of their ages be 66?

(a)  In the diagram, TU is tangent to the circle. < RVU = 100° and < URS = 36°. Calculate the value of angle STU.

(b) In triangle XYZ, |XY| = 5 cm, |YZ| = 8 cm and |XZ| = 6 cm. P is a point on the side XY such that |XP| = 2 cm and the line through P, parallel to YZ meets XZ at Q. Calculate |QZ|.

(a) A box contains 40 identical discs which are either red or white. If the probability of picking a red disc is \(\frac{1}{4}\); Calculate the number of (i) white discs ; (ii) red discs that should be added such that the probability of picking a red disc will be \(\frac{1}{3}\).

(b) A salesman bought some plates at N50.00 each. If he sold all of them for N600.00 and made a profit of 20% on the transaction, how many plates did he buy?

In the diagram, O is the centre of the circleand XY is a chord. If the radius is 5 cm and /XY/ = 6 cm, calculate, correct to 2 decimal places, the :

(a) angle which XY subtends at the centre O ;

(b) area of the shaded portion.

(a)  A boy had M Dalasis (D). He spent D15 and shared the remainder equally with his sister. If the sister's share was equal to \(\frac{1}{3}\) of M, find the value of M.

(b) A number of tourists were interviewed on their choice of means of travel. Two- thirds said that they travelled by road, \(\frac{13}{30}\) by air and \(\frac{4}{15}\) 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 (1) were interviewed ; (2) travelled by air only?