Sol. Let the M.P of 1000 gm sugar = 100 Rs.
S.P of 1000 gm of sugar = 80 Rs. (20% discount %)
But the trader give 960 gm (4% less) amount instead of 1000 gm.
Effective discount = (100 – 80/.96 )/100×100%
= 16/96 × 100%
Sol. Let the present age of man = P
According to the question,
125% (P – 10) = 831/3% (P + 10)
5/4 (P – 10) = 5/6 (P + 10)
6P – 60 = 4P + 40
2P = 100
⇒ P = 50
Q5. Find the value of tan70°.
(a) tan 40° + tan 30°
(b) 2tan 40° + tan 30°
(c) tan 50° + tan 20°
(d) 2tan 50° + tan 20°
Q6. Evaluate : 3 cos 80° cosec 10° + 2 cos 59° cosec 31°
Q9. A pole stands vertically inside a scalene triangular park ABC. If the angle of elevation of the top of the pole from each corner of the park is same, then in ABC, the foot of the pole is at the
Sol. It should be on circumcentre.
Q10. From an aeroplane just over a river, trees( having same height) on the opposite bank of the river are found to be at an angle of 60° and 30° respectively. If the breadth of the river is 400 metres, then the height of the aeroplane above the river at that instant is (Assume √3 = 1.732)
(a) 173.2 metres
(b) 346.4 metres
(c) 519.6 metres
(d) 692.8 metres
Q11. A copper wire is bent in the form of an equilateral triangle and has area 121√3 cm^2. If the same wire is bent into the form of a circle the area (in cm^2) enclosed by the wire is (take π=22/7)
Q12. One of the four angles of a rhombus is 60°. If the length of each side of the rhombus is 8 cm, then the length of the longer diagonal is
(a) 8√3 cm
(b) 8 cm
(c) 4√3 cm
(d) 8/√3 cm
Q13. Through each vertex of a triangle, a line parallel to the opposite side and cut the other lines in a middle point is drawn. the ratio of the perimeter of the new triangle thus formed, with that of the original triangle is
Q14. The area enclosed between the circumference of two concentric circles is 16𝜋 sq cm and their radii are in the ratio 5:3. What is the area of the outer circle?
(a) 9𝜋 sq cm
(b) 16𝜋 sq cm
(c) 25𝜋 sq cm
(d) 36𝜋 sq cm
Q15. A rectangle cardboard is 18 cm × 10 cm. From the four corners of the rectangle, quarter circles of radius 4 cm are cut. What is the perimeter (approximate) of the remaining portion?
(a) 47.1 cm
(b) 49.1 cm
(c) 51.0 cm
(d) 53.0 cm