Tap A can fill the empty tank in 5 minutes. When Tap A and Tap B are turned on together, they can fill the tank in 3 minutes. To find how long it takes Tap B alone to fill the tank: In 1 minute, Tap A fills 3 liters and together they fill 5 liters, so Tap B fills 2 liters in 1 minute. Since the tank holds 15 liters and Tap B fills 2 liters per minute, it will take Tap B 7.5 minutes to fill the tank alone.

1. The figure below shows square PQRS with side 13cm. T and W are the midpoints of PQ
and QR respectively. U and V are the midpoints of PS and RS respectively. Find the
total area of the shaded parts. Area of the whole figure = 13 cm 2 13 cm
x
13cm = 169 cm
13
P T 2 Q
Flip this triangle and rotate
U Remaining Area W 13cm
V R Area of rectangle = 13cm x 13cm
S x2 2 2 2 2
Remaining area= 169 cm - 169 cm = 169 cm
1 x2
2 2 2 2
x 1 2 2 2
= 338 cm - 169 cm = 169 cm ÷ 2 = 169 cm = 42.5 cm
2 2 2 2 4

2. A B
Height Height Height HeightHeight Height Height
D C
Base
1
Area of shaded triangle =
2
X Area of rectangle ABCD

3. Tap A can fill an empty tank in 5 minutes. When Tap A and Tap B are turned on
at the same time, they can fill the empty tank in 3 minutes. How long does it
take for Tab B to fill the empty tank? Assume the volume of tank as 15 Litres
Tap A 15 L Tap B
Tap A 3min
15 L 5min
4min
2min
3L 3min 5L
3L Tap B
2min 1min
5L
3L 1min
1L 30 sec
3L 5L
2L 1 min
3L 1min
2L
In 1 min , tap A + tap B fills 5Litres 2L 1 min
In 1 min , tap A fills 3Litres 1 min
2L
2L 1 min
2L 1 min
2L 1 min
In 1 min tap B fills, 2 Litres
So 15 L tap B alone, it takes 7min 30 seconds.