The Smith family paid \($5635\) for a holiday in India.
The total cost was divided in the ratio travel : accommodation : entertainment = 10 : 17 : 8.
(a) Calculate the percentage of the total cost spent on entertainment.
(b) Show that the amount spent on accommodation was \($2737.\)
(c) The \($5635\) was the total amount Mr Smith received from an investment he made 5 years ago.
Compound interest at a rate of 2.42% per year was paid on this investment.
Calculate the amount he invested 5 years ago.
(d) Mr Smith, his wife and their three children visit a theme park.
The tickets cost 2500 Rupees for an adult and 1650 Rupees for a child.
Calculate the total cost of the tickets.
(e) One day the youngest child spent 130 Rupees on sweets.
On this day the exchange rate was 1 Rupee = \($0.0152.\)
Calculate the value of the sweets in dollars, correct to the nearest cent.
▶️ Answer/Explanation
(a) Ans: 22.86%
Total ratio parts = 10 + 17 + 8 = 35.
Entertainment percentage = \(\frac{8}{35} \times 100 \approx 22.86\%\).
(b) Ans: \($2737\)
Accommodation cost = \(\frac{17}{35} \times 5635 = 2737\).
(c) Ans: \($5000\)
Using compound interest formula \(A = P(1 + r)^n\), solve for \(P\):
\(5635 = P(1.0242)^5 \implies P = \frac{5635}{(1.0242)^5} \approx 5000\).
(d) Ans: 9950 Rupees
Total cost = \(2 \times 2500\) (adults) + \(3 \times 1650\) (children) = 9950 Rupees.
(e) Ans: \($1.98\)
Value in dollars = \(130 \times 0.0152 = 1.976 \approx 1.98\).
Adele, Barbara, and Collette share \($680\) in the ratio \(9 : 7 : 4\).
(a) Show that Adele receives \($306\).
(b) Calculate the amount that Barbara and Collette each receive.
(c) Adele changes her \($306\) into euros (€) when the exchange rate is \(1 \text{ Euro} = $1.125\). Calculate the number of euros she receives.
(d) Barbara spends a total of \($17.56\) on 5 kg of apples and 3 kg of bananas. Apples cost \($2.69\) per kilogram. Calculate the cost per kilogram of bananas.
(e) Collette spends half of her share on clothes and \(\frac{1}{5}\) of her share on books. Calculate the amount she has left.
▶️ Answer/Explanation
(a) Total ratio parts = \(9 + 7 + 4 = 20\). Adele’s share = \(\frac{9}{20} \times 680 = 306\).
(b) Barbara’s share = \(\frac{7}{20} \times 680 = 238\). Collette’s share = \(\frac{4}{20} \times 680 = 136\).
(c) Euros received = \(\frac{306}{1.125} = 272\).
(d) Cost of apples = \(5 \times 2.69 = 13.45\). Cost of bananas = \(17.56 – 13.45 = 4.11\). Price per kg = \(\frac{4.11}{3} = 1.37\).
(e) Collette spends \(\frac{1}{2} \times 136 = 68\) on clothes and \(\frac{1}{5} \times 136 = 27.20\) on books. Amount left = \(136 – 68 – 27.20 = 40.80\).
Final Answer:
(a) \(306\) (shown)
(b) Barbara: \(238\), Collette: \(136\)
(c) \(272\)
(d) \(1.37\)
(e) \(40.80\)
(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 = \(\left\lfloor \frac{602.5}{8.5} \right\rfloor = 70\).
(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 \(r ≈ 6.00\%\).