Reverse percentages

           Reverse percentages

1.  Arham thinks his goldfish got chickenpox.  He lost 70% of his collection of goldfish. If he has 60

   survivors, how many did he have originally?

2. When heated an iron bar expands by 0.2%. If the increase in length is 1 cm, What is the original 

   length of the bar?

3. A one year old car is worth $11250. If its value had depreciated by 25% in that first year, calculate its price when new.

4. A sterio system is sold for $1998 and an 11% profit made. Find the original cost of the stereo.

5. A dealer gains5%  by selling a washing machine for $950. Find the original cost of the washing machine.

6. A dealer bought a second hand car and spent $650 on repairs. He made a profit of 20% by selling the car for $18 650. For how much did he purchase it?

7. By selling a set of Biology books for $408, the book seller suffers a loss of 4%. What was the cost price of the books?

8. A television has a sale price of $180. This is a saving of 25% on the original price. Find the original price.

9. A company increased its productivity by10% each year for the last two years. If it produced 56 265 units this year, how many units did it produce two years ago?

10. This year a farmer’s crop yielded 50 000 tonnes. If this represents a 25% increase on last year, what was the yield last year?

Angles of elevation and depression

Grade 9           Angles of elevation and depression                                                                 work sheet

(1) In order to find the height of a tree, some children walk 50 m from the base of the tree and measure the angle of elevation as 10^o. Find the height of the tree.

(2) A man standing on top of a mountain 1200 m high observes the angle of depression of a steeple to be 43^o. How far is the steeple from the mountain?

(3) A ladder is placed on horizontal ground with its foot 2 m from a vertical wall. If the ladder makes an angle of 50^o with the ground, find (a) the length of the ladder, 

     (b) the height of the wall. Give answers correct to 1 d.p.

(4) The length of the shadow of a vertical pole is 3.42m long when the rays of the sun are inclining at an angle of 40.5^o to the horizontal. What is the height of the pole?

 Give answer to 2 d.p.

X

(5) A boy X can be seen by two of his friends Y and Z, who are swimming in the sea.

40 m

      If the angle of elevation of X from Y is 23^o and from Z is 32^o, and the height of X

      above Y and Z is 40m. Calculate the horizontal distance:

      (i)  between X and Z.                     (ii) between X and Y              

      (iii) between Y and Z.

(6) A radio mast of 30m high is supported by two cables as shown.

      From the diagram:

        (i) find the distance between the two points A and B.

(1) The height of a tower is 15 m. A man looks at the tower from a distance of 120m. What is the angle of elevation of the top of the tower from man?
(2) Find the angle of depression ao of the structure.
(3) The height of a tree is 25 m. The shadow of the tree has a length of 30 m. Calculate the size of the angle marked po in the diagram
(4) A hot air balloon, M, is 900m vertically above a point N on the ground.      A boy stands at a point O, 1200m  horizontally from N.                  (a) Calculate the distance, OM, of the boy from the balloon.                  (b) Calculate the angle MON.
(5) A and B are two villages. If the horizontal distance between them is 12km and the vertical distance between them is 2 km, calculate:      (i) the shortest distance between the two villages,      (ii) the angle of elevation of B and A.
(6) A man at the top of a vertical cliff observes a boat (B) at sea. From the diagram,                 (i) State the angle of depression of the boat from the man.                 (ii) How far is the boat from the cliff?
(7) Two planes A and B are flying directly above each other. A person (P) can see both of them. The vertical height between B and P is 5 km. if the angles of elevation of the planes        from person are 65o and 75o, calculate:        (i) horizontal distance of P from the two planes.        (ii) the vertical distance between A and B.

(8) Two people A and B are standing either side of a transmission mast.

      A is 130m away from the mast and B is 200m away.

      If the angle of elevation of the top of the mast from A is 60^o.

      Calculate

     (i) the height of the mast

     (ii) the angle of elevation of the top of the mast from B.

 (9) A girl standing on a hill at A, overlooking a lake, can see a small boat at a point B on the lake.

 If the girl is at a height of 50m above B and at a horizontal

 distance of 120m away from B, calculate:

(i) the angle of depression of the boat from the girl,

(ii) the shortest distance between the girl and the boat.

# Note : Teachers are required to provide suitable diagrams for the questions

percentage and money exchange - Japan

1. Japan's population is estimated at around 127 million.

  (a) Write  Japan's population in standard form

  There are about 136,000 Western expatriates.

  (b) What percentage of the Western expatriates are in Japan?

   About 19.5 percent of the population was over 65 years of age.

  (c) Find the number of people who are below 65.

The Japanese population is rapidly aging as a result of a post–World War II baby boom followed by a decrease in birth rates. A growing number of younger Japanese prefer not to marry or have families. Hence Japan's population is expected to drop to 100 million by 2050 and to 64 million by 2100.

(d) Calculate the expected percentage decrease in population in the year 2050 and 2100.

Japan's legislative organ is the National Diet, a bicameral parliament. The Diet consists of a House of Representatives with 480 seats, and a House of Councilors of 242 seats.

(e) Express the number of House of councilors seats as a percentage of the total number of seats.
........

2. The Asakusa Samba Carnival is held annually, on a Saturday towards the end of August, in Asakusa, Tokyo.  The cost of tickets for Adults     -  350 JPY and Children -  150 JPY

The carnival starts at 7.15 am everyday and closes at 11.30 pm.

2000 Adults and 6000 Children attended on the first day

a) Calculate the amount of money they got by selling the tickets

               (i) To adults                                                                                                                                   

              (ii) To children  

              (iii) The total amount           

  b) Calculate the percentage of the amount of money collected from children.

 c) Convert the above total amount to dollars, if $1 = 80.86 JPY.

 d) Convert the timing to 24 hr clock time.                          

 e) Calculate the duration of the carnival in a day                

 f) Mrs. Carolene has got some dollars with her. How many dollars she has to pay to enter the           carnival along with her two kids. If  $1 = 80.86 JPY