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
(a) A box is a cuboid with length 45cm, width 30cm and height 42cm.
The box is completely filled with 90.72kg of sand.
Calculate the density of this sand in \(kg/m^{3}.\)
[Density = mass ÷ volume]
………………………………… \(kg/m^{3}\)
(b) A bag contains \(15000cm^3\)
of sand.
Some of this sand is used to completely fill a hole in the shape of a cylinder.
The hole is 30cm deep and has radius 10cm.
Calculate the percentage of the sand from the bag that is used.
……………………………………….%
(c) Sand costs \($98.90\) per tonne.
This cost includes a tax of 15%.
Calculate the amount of tax paid per tonne of sand.
\($ ………………………………………….\)
(d) Raj buys some sand for 3540 rupees.
Calculate the cost in dollars when the exchange rate is \($1\) = 70.8 rupees.
\($ ………………………………………….\)
Answer/Explanation
(a) 1600
(b) 62.8 or 62.83 to 62.84
(c) 12.9[0]
(d) 50
Question
These are the rates charged by a painter, a plumber and an electrician who do some work for Mr Sharma.
(a) The painter works for 7 hours.
Calculate the amount Mr Sharma pays the painter.
\($ ………………………………………….\)
(b) Mr Sharma pays the plumber \($252.\)
Calculate how many hours the plumber works.
…………………………………. hours
(c) Mr Sharma pays the electrician \($224.\)
Calculate how many hours the electrician works
…………………………………. hours
(d) Write down the ratio of the amount Mr Sharma pays to the painter, the plumber and the electrician.
Give your answer in its lowest terms.
painter : plumber : electrician = ……………… : ……………… : ………………
Answer/Explanation
(a) 245
(b) 8
(c) 6
(d) 35 : 36 : 32 final answer