(a) Dhanu has a model railway.
(i) 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. Work out the total mass of the train.
(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.
(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.
(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 1115. 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.
▶️ Answer/Explanation
(a)(i) Ans: 295 g
Total mass = Locomotive + 4 Coaches = \(87 + 4 \times 52 = 87 + 208 = 295\) g.
(a)(ii) Ans: 29.5%
Percentage = \(\left(\frac{87}{295}\right) \times 100 ≈ 29.5\%\).
(b) Ans: 11 cm
Total distance covered = Speed × Time = \(18 \times 4 = 72\) cm. Bridge length = Total distance – Train length = \(72 – 61 = 11\) cm.
(c) Ans: 4160 rupees
Cost in rupees = \(\frac{64}{0.0154} ≈ 4155.84\), rounded to nearest 10 rupees = 4160.
(d) Ans: $2.40
Let original cost = \(P\). \(1.125P = 2.70\), so \(P = \frac{2.70}{1.125} = 2.40\).
(e) Ans: 53 : 36
Time playing = 4 hours 25 minutes = 265 minutes. Time cycling = 3 hours = 180 minutes. Ratio = \(265 : 180 = 53 : 36\) (simplified).
(f) Ans: 6.00%
Using exponential growth formula: \(550 \times (1 + \frac{r}{100})^5 = 736\). Solving gives \(r ≈ 6.00\%\).
(a) A shop sells dress fabric for \($\)2.97 per metre.
(i) A customer buys 9 metres of this fabric.
Calculate the change he receives from \($\)50.
(ii) The selling price of \($\)2.97 per metre is an increase of 8% on the cost price.
Calculate the cost price.
(b) A dressmaker charges \($35\) or 2300 rupees to make a dress.
Calculate the difference in price when the exchange rate is 1 rupee=\($\)0.0153.
Give your answer in rupees.
(c) The dressmaker measures a length of fabric as 600m, correct to the nearest 5 metres.
He cuts this into dress lengths of 9m, correct to the nearest metre.
Calculate the largest number of complete dress lengths he could cut.
▶️ Answer/Explanation
(a)(i) Ans: $23.27
Total cost = \(9 \times 2.97 = 26.73\). Change = \(50 – 26.73 = 23.27\).
(a)(ii) Ans: $2.75
Let cost price = \(x\). Then, \(1.08x = 2.97\), so \(x = \frac{2.97}{1.08} = 2.75\).
(b) Ans: 12.41 rupees
Convert \($35\) to rupees: \(35 \div 0.0153 \approx 2287.58\). Difference = \(2300 – 2287.58 = 12.42\) rupees.
(c) Ans: 70
Max fabric length = 602.5m (nearest 5m). Min dress length = 8.5m (nearest metre). Largest number = \(\left\lfloor \frac{602.5}{8.5} \right\rfloor = 70\).