On selling a pencil-box at ^@40 \%^@ gains and glass-box at ^@50 \%^@ gain, a seller gains ^@R 17^@. If he sells the pencil-box at ^@40 \%^@ gain and glass-box at ^@70 \%^@ gain, he gains ^@R 23^@. Find the actual price of pencil-box and glass-box .
A family has 450 kg of rice for x number of weeks. If they need to use same amount of rice for 3 more weeks, they need to cut down their weekly consumption of rice by 5 kgs. Find value of x.
Two poles of heights ^@ 27 \space metres^@ and ^@51 \space metres^@ stand vertically on a plane ground. If the distance between their feet is ^@32 \space metres^@, find the distance between their tops.
Without using trignometric tables, evaluate the value of ^@tan {\space} 27^\circ tan {\space} 63^\circ + cot {\space} 63^\circ cot {\space} 27^\circ ^@.
In the given figure, ^@ XY ^@ and ^@ X'Y' ^@ are two parallel tangents to a circle with center ^@ O ^@ and another tangent ^@ AB ^@ with the point of contact ^@ C ^@ intersects ^@ XY ^@ at ^@ A ^@ and ^@ X'Y' ^@ at ^@ B ^@. Find the measure of ^@ \angle AOB ^@.
Find the difference between the area of a regular hexagonal plot each of whose side is ^@ 52 \space m ^@ and the area of the circular swimming tank inscribed in it. ^@ \bigg[π = \dfrac { 22 } { 7 } \text { and } \sqrt { 3 } = 1.732 \bigg]^@
A wooden article was made by scooping out a hemisphere from each end of a cylinder as shown in the figure. If the height of the cylinder 34 cm and its base is of radius 4 cm, then the total surface area of the article when it is ready is:
A box contains 4 purple and 4 blue balls. Megan takes out a ball, puts it back, and then takes out another ball. What is the probability that both balls were purple?
South Africa
