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11+ · Number and Problem Solving

EP.M105 Direct Proportion and Value for Money

GL ASSESSMENT GL-11PLUS-MATHS · Calculators not allowed · about 55 minutes

Total Marks

Name: _______________________________ Date: ____ / ____ / ______

Answer ALL questions. Show all your working.

Six apples cost 90p. What is the cost of one apple?

A) 15p
B) 14p
C) 18p
D) 150p
E) 1.5p

(Total for Question 1 is 1 mark)

Three chocolate bars cost £1.35. What is the price of one bar?

A) 45p
B) 55p
C) 40p
D) 35p
E) 50p

(Total for Question 2 is 1 mark)

A 5 kg sack of flour costs £7.50. What is the cost per kilogram?

A) £0.75
B) £1.50
C) £2.50
D) £15.00
E) £0.15

(Total for Question 3 is 1 mark)

An item costs £4.00. The shop runs a 'buy one, get a second at 50% off' offer. How much would two of the items cost under this offer?

A) £6.00
B) £5.00
C) £8.00
D) £4.50
E) £2.00

(Total for Question 4 is 1 mark)

A 250 g tin of baked beans costs 40p. What is the price per 100 g?

A) 16p
B) 10p
C) 25p
D) 18p
E) 12p

(Total for Question 5 is 1 mark)

A 1 L bottle of water costs £1.20. A smaller 500 ml bottle costs 70p. Which bottle gives the cheaper price per litre?

A) The 1 L bottle
B) The 500 ml bottle
C) They are the same
D) Cannot tell
E) Cheaper per 250 ml

(Total for Question 6 is 1 mark)

Cereal A costs £2.40 for 400 g. Cereal B costs £2.90 for 500 g. Which cereal is cheaper per 100 g?

A) Cereal A
B) Cereal B
C) They cost the same
D) Cereal A is twice the price of B
E) Cannot tell

(Total for Question 7 is 1 mark)

A 750 ml bottle of cordial costs £1.80. What is the price per litre?

A) £2.40
B) £1.35
C) £3.60
D) £1.20
E) £2.25

(Total for Question 8 is 1 mark)

A bakery offers 3 muffins for £2.00. What is the price of one muffin (to the nearest hundredth of a pound)?

A) £0.66
B) £0.67
C) £0.60
D) £0.75
E) £0.70

(Total for Question 9 is 1 mark)

A jar normally contains 400 g of jam. A promotion gives 20% extra free for the same price. How many grams are in the promotional jar?

A) 480 g
B) 420 g
C) 460 g
D) 520 g
E) 400 g

(Total for Question 10 is 1 mark)

How many 250 g packets are needed to make 3 kg?

A) 10
B) 11
C) 12
D) 13
E) 14

(Total for Question 11 is 1 mark)

A supermarket sells 6 muffins for £3.00. What is the cost of one muffin?

A) 40p
B) 45p
C) 50p
D) 60p
E) 55p

(Total for Question 12 is 1 mark)

A 500 g bag of rice costs £1.80. Work out the cost of 1 kg of rice.

(Total for Question 13 is 2 marks)

Four pencils cost 75p. How many pencils can you buy for £3.00?

(Total for Question 14 is 2 marks)

A 400 ml bottle of shampoo costs £3.20. The shop sells two 600 ml bottles for £5.60. Which offer gives better value per millilitre? Show your working.

(Total for Question 15 is 3 marks)

A box of cereal is 500 g and costs £2.40. It is sold with 25% extra free. (a) How many grams are in the promotional box? (b) What is the price per 100 g in the promotional box? Give your answer in pence to one decimal place.

(a)How many grams are in the promotional box?(1)

(b)What is the price per 100 g in the promotional box? Give answer to one decimal place in pence.(1)

(Total for Question 16 is 2 marks)

Priya sees an offer: 3 chocolate bars for £2.10. There is also a store discount of 20% off the total when you buy 5 or more bars. How much would she pay for 6 bars with the discount?

(Total for Question 17 is 2 marks)

A pen costs £1.25 each. A pack of 5 pens costs £5.60. The shop offers a loyalty voucher giving 10% off packs only. Using the voucher, what is the price per pen if you buy the 5-pack? Which is cheaper, a single pen or a pen from the discounted pack?

(Total for Question 18 is 3 marks)

A 750 ml bottle of juice costs £2.25. A larger 1.5 L bottle costs £3.80. Which bottle is cheaper per litre? Show your working.

(Total for Question 19 is 2 marks)

A toy shop sells small packs of 4 toys for £3.20 and large packs of 10 toys for £7.50. The shop runs a promotion: for every 3 large packs bought, you receive one small pack free. A customer needs 50 toys. Work out the least possible cost for the customer. Show your calculations.

(Total for Question 20 is 4 marks)

Mark scheme · EP.M105 Direct Proportion and Value for Money

Question 1

B1 correct option A (15p) cao
Answer: A) 15p (90p ÷ 6 = 15p per apple). The cost of one apple is 15p.

Question 2

B1 correct option A (45p) cao
Answer: A) 45p (£1.35 ÷ 3 = £0.45 = 45p)

Question 3

B1 correct option B (£1.50) cao
Answer: B) £1.50 (£7.50 ÷ 5 = £1.50 per kg)

Question 4

B1 correct option A (£6.00) cao
Answer: A) £6.00 (first at £4.00, second at 50% of £4.00 = £2.00; total £6.00)

Question 5

B1 correct option A (16p per 100 g) cao
Answer: A) 16p (40p ÷ 250 g × 100 g = 16p per 100 g)

Question 6

B1 correct option A (the 1 L bottle) cao
Answer: A) The 1 L bottle (£1.20 per L versus 70p for 0.5 L = £1.40 per L)

Question 7

B1 correct option B (Cereal B) cao
Answer: B) Cereal B (Cereal A: 240p ÷ 4 = 60p per 100 g; Cereal B: 290p ÷ 5 = 58p per 100 g)

Question 8

B1 correct option A (£2.40 per litre) cao
Answer: A) £2.40 (£1.80 ÷ 0.75 L = £2.40 per litre)

Question 9

B1 correct option B (£0.67) cao
Answer: B) £0.67 (£2.00 ÷ 3 approx £0.6667, rounded to £0.67)

Question 10

B1 correct option A (480 g) cao
Answer: A) 480 g (400 g + 20% of 400 g = 400 + 80 = 480 g)

Question 11

B1 correct option C (12 packets) cao
Answer: C) 12 (3 kg = 3000 g; 3000 ÷ 250 = 12)

Question 12

B1 correct option C (50p) cao
Answer: C) 50p (£3.00 ÷ 6 = £0.50 = 50p)

Question 13

M1 use of unitary method or recognition that 1 kg is two 500 g bags (1.80 x 2 seen) isw
A1 £3.60 cao
Answer: £3.60 (500 g costs £1.80 so 1 kg = 2 × £1.80 = £3.60)

Question 14

M1 use of scaling or unitary method to find number of pencils (e.g. 75p for 4 implies 300p for 16) ft
A1 16 pencils cao
Answer: 16 pencils (75p × 4 = 300p so £3.00 buys 4 × 4 = 16 pencils)

Question 15

M1 correct method for single bottle: 320p ÷ 400 = 0.8 p per ml seen
M1 correct method for two-bottle deal: 560p ÷ 1200 = 0.4666... p per ml seen
A1 conclusion that the two-for-£5.60 deal is better value cao
Answer: Two-for deal is better value. Single: 320p ÷ 400 ml = 0.8 p/ml. Two for £5.60: 560p ÷ 1200 ml approx 0.4667 p/ml. The two-bottle offer is cheaper per ml.

Question 16

(a) B1 625 g cao
(a) Answer: 625 g
(b) A1 38.4p per 100 g cao
(b) Answer: 38.4p per 100 g

Question 17

M1 full price for 6 bars found: 6 × £0.70 = £4.20 seen
A1 £3.36 cao (20% off £4.20 gives £3.36)
Answer: £3.36 (3 for £2.10 -> £0.70 each; 6 × £0.70 = £4.20; 20% off -> 80% × £4.20 = £3.36)

Question 18

M1 correct calculation of pack after voucher: £5.60 × 0.90 = £5.04 seen
M1 correct division to give per pen: £5.04 ÷ 5 = £1.008 seen
A1 conclusion that the discounted pack gives cheaper pens at about £1.01 each cao
Answer: Discounted pack is cheaper. £5.60 × 0.90 = £5.04; £5.04 ÷ 5 = £1.008 -> about £1.01 per pen, cheaper than £1.25 single pen.

Question 19

M1 correct calculation of unit prices: £2.25 ÷ 0.75 = £3.00; £3.80 ÷ 1.5 approx £2.53
A1 conclusion that the 1.5 L bottle is cheaper per litre cao
Answer: 1.5 L bottle is cheaper. 750 ml: £2.25 ÷ 0.75 L = £3.00 per L. 1.5 L: £3.80 ÷ 1.5 L approx £2.53 per L.

Question 20

M1 correct use of the promotion to find toys from 3 large packs: 3 × 10 = 30 plus one free small pack = 34 toys seen
M1 correct cost calculation for 3 large packs: 3 × £7.50 = £22.50 seen
M1 correct calculation of additional small packs needed and their cost: need 16 more toys -> 4 small packs cost 4 × £3.20 = £12.80 seen
A1 final minimum cost given as £35.30 cao with correct justification
Answer: Least cost £35.30. Buy 3 large packs (£22.50) which gives 30 toys plus one free small pack (4) = 34 toys. Need 16 more -> 4 small packs at £3.20 = £12.80. Total £22.50 + £12.80 = £35.30.

Direct Proportion and Value for Money - Worksheets, Questions and Revision