Worded Problems Set B Worksheet with Answers

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11+ · GL ASSESSMENT

EP.M22 Worded Problems Set B

GL ASSESSMENT GL-11PLUS-MATHS · Calculators not allowed · about 60 minutes

Total Marks

Name: _______________________________ Date: ____ / ____ / ______

Answer ALL questions. Show all your working.

1

Elif buys a magazine for £2.60 and a bottle of water for £0.75. She pays with a £5 note. How much change does she get?

A) £1.35
B) £1.45
C) £1.55
D) £1.65
E) £1.85

(Total for Question 1 is 1 mark)

2

A swimming lesson starts at 16:10 and lasts 45 minutes. What time does it finish?

(Total for Question 2 is 1 mark)

3

A charity shop sells a jacket for £18. A buyer is given a discount voucher worth 1/3 of that amount, to use on a future purchase. How much is the voucher worth?

A) £3
B) £6
C) £9
D) £12
E) £15

(Total for Question 3 is 1 mark)

4

In a school choir, the ratio of boys to girls is 2:5. There are 8 boys in the choir. How many girls are there?

(Total for Question 4 is 1 mark)

5

Find the mean of these five numbers: 4, 6, 6, 8, 11.

A) 6
B) 6.5
C) 7
D) 7.5
E) 11

(Total for Question 5 is 1 mark)

6

Marcus buys 4 plant pots at £1.35 each and a bag of compost for £3.60. He pays with a £10 note. How much change does he receive?

(Total for Question 6 is 2 marks)

7

Aoife and Jamal buy raffle tickets in the ratio 3:4. Together they buy 35 tickets. How many more tickets does Jamal buy than Aoife?

A) 1
B) 5
C) 15
D) 20
E) 35

(Total for Question 7 is 2 marks)

8

A drama rehearsal starts at 15:50 and lasts for 1 hour 20 minutes. The performers then have a 10 minute break before the next rehearsal starts. What time does the next rehearsal start?

(Total for Question 8 is 2 marks)

9

Freya cycles at a steady speed of 18 km/h. How far does she travel in 50 minutes?

A) 9 km
B) 12 km
C) 13.5 km
D) 15 km
E) 16.5 km

(Total for Question 9 is 2 marks)

10

A coat originally costs £64. In a sale, 1/4 is taken off the price. What is the sale price?

(Total for Question 10 is 2 marks)

11

Four friends have a mean of £15 in their savings jars. Dawit, Isla and Ravi have £12, £18 and £14 in their jars. How much does the fourth friend, Poppy, have?

A) £12
B) £14
C) £15
D) £16
E) £18

(Total for Question 11 is 2 marks)

12

Amir thinks of a number. He trebles it, then subtracts 9, and the result is 30. What number did Amir think of?

(Total for Question 12 is 2 marks)

13

A jug holds 1.8 litres of water. Lucia pours the water equally into 6 identical glasses. How many millilitres of water go into each glass?

A) 30 ml
B) 180 ml
C) 200 ml
D) 300 ml
E) 360 ml

(Total for Question 13 is 2 marks)

14

A rectangular vegetable patch is 7.5 m long and 4 m wide. Connor wants to put fencing all the way around the patch, but leaves a 1.5 m gap for a gate. How many metres of fencing does he need?

(Total for Question 14 is 2 marks)

15

A model train is built to a scale of 1:75. The real locomotive is 12 m long. How long is the model, in centimetres?

A) 9 cm
B) 12 cm
C) 16 cm
D) 18 cm
E) 25 cm

(Total for Question 15 is 2 marks)

16

A train timetable shows trains leaving every 24 minutes, starting at 07:12. What is the departure time of the 6th train of the day?

(Total for Question 16 is 2 marks)

17

A 500 g box of cereal costs £2.30, and a 750 g box costs £3.15. Which box offers better value for money, and what is its price per 100 g?

A) 500 g box at 40p per 100 g
B) 500 g box at 46p per 100 g
C) 750 g box at 42p per 100 g
D) 750 g box at 45p per 100 g
E) Both are the same value, at 44p per 100 g

(Total for Question 17 is 2 marks)

18

Salma is 4 years older than her brother Ollie. In 6 years' time, the sum of their ages will be 42. How old is Ollie now?

(Total for Question 18 is 2 marks)

19

A school trip costs £84 per pupil. Erin's parents pay a £20 deposit, then the rest in equal monthly instalments over 4 months.

(a)How much is left to pay after the deposit?(1)

(b)How much is each monthly instalment?(2)

(Total for Question 19 is 3 marks)

20

A school fete raises £160. 1/4 of the money is spent on prizes, and the remainder is split between two charities in the ratio 5:3. How much does the charity with the larger share receive?

A) £45
B) £60
C) £100
D) £75
E) £90

(Total for Question 20 is 3 marks)

21

On 22/09, Hassan drives to a warehouse 90 km away at an average speed of 60 km/h. He leaves home at 08:40.

(a)At what time does he arrive at the warehouse?(1)

(b)He stays at the warehouse for 40 minutes, then drives home again, this time at an average speed of 45 km/h because of traffic. At what time does he get home?(2)

(Total for Question 21 is 3 marks)

22

A library orders 270 new books. 2/9 of the books are for younger readers, 1/3 are for teenagers, and the rest are for adults. How many more adult books are ordered than younger-reader books?

A) 30
B) 40
C) 60
D) 90
E) 120

(Total for Question 22 is 3 marks)

23

A theatre has 10 rows of seats, with the same number of seats in each row. If 4 more seats were added to each row, the theatre would hold 300 seats in total.

(a)How many seats are currently in each row?(2)

(b)How many seats does the theatre currently hold in total?(1)

(c)Instead, suppose no seats are added to each row, but 2 extra rows (each holding the original number of seats) are added to the theatre. How many seats would the theatre hold in total?(1)

(Total for Question 23 is 4 marks)

24

Six cousins, Kai, Siobhan, Femi, Rosa, Charlotte and Deepak, share money from selling old toys in the ratio 1:2:2:3:4:6 respectively. The mean amount received across all six cousins is £9.

(a)What is the total amount of money shared?(2)

(b)How much did Charlotte receive?(2)

(Total for Question 24 is 4 marks)

25

At 10:00, Poppy and Tomasz start cycling towards each other along a straight cycle path that is 27 km long, starting from opposite ends at the same time. Poppy cycles at 15 km/h and Tomasz cycles at 12 km/h.

(a)What is their combined speed of approach, in km/h?(1)

(b)At what time do they meet?(2)

(Total for Question 25 is 3 marks)

Mark scheme · EP.M22 Worded Problems Set B

Question 1

B1 D) £1.65, from £5.00 - £3.35
Answer: D) £1.65

Question 2

B1 16:55
Answer: 16:55

Question 3

B1 B) £6, from 18 / 3
Answer: B) £6

Question 4

B1 20 girls, with correct scaling shown or implied
Answer: 20 girls

Question 5

B1 C) 7, from a total of 35 divided by 5 numbers
Answer: C) 7

Question 6

M1 finds total cost 4 x £1.35 + £3.60 = £9.00
A1 £1.00, from £10.00 - £9.00
Answer: £1.00

Question 7

M1 total parts = 7, one part = 35 / 7 = 5
A1 B) 5 (Jamal 20 - Aoife 15)
Answer: B) 5

Question 8

M1 finds the end of the first rehearsal = 17:10
A1 17:20, after adding the 10 minute break
Answer: 17:20

Question 9

M1 50 minutes = 5/6 hour
A1 D) 15 km (18 x 5/6)
Answer: D) 15 km

Question 10

M1 finds the discount = 64 / 4 = £16
A1 £48
Answer: £48

Question 11

M1 total = 4 x 15 = 60; known total = 12 + 18 + 14 = 44
A1 D) £16 (60 - 44)
Answer: D) £16

Question 12

M1 30 + 9 = 39
A1 13
Answer: 13

Question 13

M1 converts 1.8 litres to 1800 ml
A1 D) 300 ml (1800 / 6)
Answer: D) 300 ml

Question 14

M1 perimeter = 2 x (7.5 + 4) = 23 m
A1 21.5 m, after subtracting the 1.5 m gate
Answer: 21.5 m

Question 15

M1 converts 12 m to 1200 cm
A1 C) 16 cm (1200 / 75)
Answer: C) 16 cm

Question 16

M1 the 6th train is 5 intervals after the 1st, so 5 x 24 = 120 minutes after 07:12
A1 09:12
Answer: 09:12

Question 17

M1 finds both unit prices: 500 g = 46p per 100 g, 750 g = 42p per 100 g
A1 C) 750 g box at 42p per 100 g
Answer: C) 750 g box at 42p per 100 g

Question 18

M1 sets up (x + 6) + (x + 10) = 42, or equivalent, giving 2x + 16 = 42
A1 13 years old
Answer: 13 years old

Question 19

(a) B1 £64
(a) Answer: £64
(b) M1 identifies £64 remaining, to be split over 4 months
(b) A1 £16 per month (64 / 4)
(b) Answer: £16

Question 20

M1 prizes = 1/4 x 160 = £40; remainder = 160 - 40 = £120
M1 ratio parts total 8, one part = 120 / 8 = £15
A1 D) £75 (5 x £15)
Answer: D) £75

Question 21

(a) B1 10:10
(a) Answer: 10:10
(b) M1 finds departure time after the break (10:10 + 0:40 = 10:50) and the return journey time (90 / 45 = 2 hours)
(b) A1 12:50
(b) Answer: 12:50

Question 22

M1 younger = 2/9 x 270 = 60 and teenagers = 1/3 x 270 = 90
M1 adults = 270 - 60 - 90 = 120
A1 C) 60 (120 - 60)
Answer: C) 60

Question 23

(a) M1 300 / 10 = 30 (seats per row if 4 were added)
(a) A1 26 seats per row
(a) Answer: 26 seats per row
(b) B1 260 seats
(b) Answer: 260 seats
(c) B1 312 seats
(c) Answer: 312 seats

Question 24

(a) M1 total = mean x 6
(a) A1 £54
(a) Answer: £54
(b) M1 total ratio parts = 1 + 2 + 2 + 3 + 4 + 6 = 18, one part = 54 / 18 = £3
(b) A1 £12 (Charlotte's 4 parts x £3)
(b) Answer: £12

Question 25

(a) B1 27 km/h
(a) Answer: 27 km/h
(b) M1 time = distance / combined speed = 27 / 27
(b) A1 11:00 (1 hour after 10:00)
(b) Answer: 11:00

Worded Problems Set B - Worksheets, Questions and Revision

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EP.M22 Worded Problems Set B

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Question 10

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Question 12

Question 13

Question 14

Question 15

Question 16

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Question 19

Question 20

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Question 23

Question 24

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Question 11

Question 12

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Question 15

Question 16

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Question 18

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Question 21

Question 22

Question 23

Question 24

Question 25