iGCSE Mathematics (0580) :C1.15 Calculate using money and convert from one currency to another . iGCSE Style Questions Paper 3

(a)(i): $12~07$
(a)(ii): 10:27 drawn correctly on clock face.
(b): $21$
(c): $57.75$ (and later corrected to $45$)
(d)(i): $232$
(d)(ii): $125$
(d)(iii): The number of workers who travel to work by train but who do not travel on a bus.
(d)(iv): $\frac{9}{232}$ (e) 45

Detailed Answer

(a)(i)
The train leaves Hinton at 10:47.
The next train reaches Jarmouth at 12:35, and the previous train reaches Jarmouth at 11:15.

$
12:35 – 11:15 = 1 \text{ hour 20 minutes} (80 \text{ minutes})
$

Add 80 minutes to the departure time (10:47)
$
10:47 + 1 \text{ hour 20 minutes} = 12:07
$
(ii)

Marge arrives20 minutes before 10:47,

$
10:47 – 20 = 10:27
$

(b)
First bus:07:10
Last bus:22:10
Interval: Every45 minutes

From07:10 to 22:10 is15 hours:

$
15 \times 60 = 900 \text{ minutes}
$
count all the buses, include the first one:
$
\frac{900}{45} + 1 = 20 + 1 = 21
$

(c)
1.2022 Cost:$\$50$

2023 (10% increase):
$
50 + (50 \times 0.10) = 50 + 5 = 55
$

2024 (5% increase):
$
55 + (55 \times 0.05) = 55 + 2.75 = 57.75
$

Cost on 1st Jan 2024:$\$57.75$

(d)
Workers who travel by bus only (B) = 31
Workers who travel by train only (T) = 85
Workers who travel by both bus and train (B ∩ T) = 9
Workers who don’t travel by bus or train = 107

(i)

Total workers = (Bus only) + (Train only) + (Both) + (Neither)
$
= 31 + 85 + 9 + 107 = 232
$

(ii)
$
n(B ∪ T) = (Bus only) + (Train only) + (Both)
$
$
= 31 + 85 + 9 = 125
$

(iii)
The number 85 represents the workers who travel to work by train only, not using the bus.

(iv)
$
\text{Probability} = \frac{\text{Number of workers traveling by both}}{\text{Total number of workers}}
$
$
= \frac{9}{232}
$

(e)

The number of single rooms as 3x and double rooms as 8x.

The difference is 75
$
8x – 3x = 75
$
$
5x = 75
$
$
x = 15
$

Single rooms = 3 × 15 = 45
Double rooms = 8 × 15 = 120
So, the number of single rooms is 45.