Question
(a) Manjeet uses 220 litres of water each day.
She reduces the amount of water she uses by 15%.
Calculate the number of litres of water she now uses each day.
………………………………….. litres
(b) Manjeet has two mathematically similar bottles in her bathroom.
The large bottle holds 1.35 litres and is 29.7cm high.
The small bottle holds 0.4 litres.
Calculate the height of the small bottle
…………………………………….. cm
(c) Water from Manjeet’s shower flows at a rate of 12 litres per minute.
The water from the shower flows into a tank that is a cuboid of length 90cm and width 75cm.
Calculate the increase in the level of water in the tank when the shower is used for 7 minutes.
…………………………………….. cm
Answer/Explanation
(a) 187
(b) 19.8
(c) 12.4 or 12.44…
Question
Dhanu has a model railway.
(a) He has a train that consists of a locomotive and 4 coaches.
The mass of the locomotive is 87g and the mass of each coach is 52g.
(i) Work out the total mass of the train.
………………………………………. g
(ii) Work out the mass of the locomotive as a percentage of the total mass of the train.
……………………………………… %
(b) The train is 61cm long and travels at a speed of 18cm/s.
It takes 4 seconds for the whole of the train to cross a bridge.
Calculate the length of the bridge.
……………………………………. cm
(c) A new locomotive costs \($64.\)
Calculate the cost of the locomotive in rupees when the exchange rate is 1 rupee = \($0.0154 .\)
Give your answer correct to the nearest 10 rupees.
……………………………….. rupees
(d) The cost of a railway magazine increases by 12.5% to \($2.70 .\)
Calculate the cost of the magazine before this increase.
\($ ………………………………………….\)
(e) Dhanu plays with his model railway from 0650 to 11 15.
He then rides his bicycle for 3 hours.
Find the ratio time playing with model railway : time riding bicycle.
Give your answer in its simplest form.
……………………. : …………………….
(f) The value of Dhanu’s model railway is \($550.\)
This value increases exponentially at a rate of r% per year.
At the end of 5 years the value will be \($736.\)
Calculate the value of r.
r = ………………………………………….
Answer/Explanation
(a)(i) 295
(a)(ii) 29.5 or 29.49…
(b) 11
(c) 4160
(d) 2.4[0]
(e) 53 : 36
(f) 6[.00] or 5.999…
Question
Two rectangular picture frames are mathematically similar.
(a) The areas of the frames are \(350 cm^{2) and \(1134 cm^{2}\). The width of the smaller frame is 17.5cm.
Calculate the width of the larger frame.
(b) A picture in the smaller frame has length 15cm and width 10.5cm, both correct to the nearest 5mm.
Calculate the upper bound for the area of this picture.
(c) In a sale, the price of a large frame is reduced by 18%. Parthi pays $166.05 for 5 large frames in the sale.
Calculate the original price of one large frame.
(d) Parthi advertises a large frame for a price of $57 or 48.20 euros. The exchange rate is $1= 0.88 euros.
Calculate the difference between these prices, in dollars and cents, correct to the nearest cent.
Answer/Explanation
7(a) 31.5
7(b) 163.9375 or \(163\frac{15}{16}\) final answer
7(c) 40.5[0]
7(d) $2.23 final answer