Sasi Math (Revised for 1024)

Scroll:Distance, Time and Speed >> Distance, Time & Speed >> ps (1770)

Written Instructions:

For each Multiple Choice Question (MCQ), four options are given. One of them is the correct answer. Make your choice (1,2,3 or 4). Write your answers in the brackets provided..

For each Short Answer Question(SAQ) and Long Answer Question(LAQ), write your answers in the blanks provided.

Leave your answers in the simplest form or correct to two decimal places.

Town Lala and Town Yaya are 720 km apart. At 8.30 a.m., a car left Town Lala for Town Yaya, travelling at a constant speed. At the same time, a lorry set off from Town Yaya for Town Lala at a constant speed too. At 1.30 p.m.,the two vehicles passed each other. If the speed of the car was 12 $\frac{km}{h}$ faster than the lorry, find the speed of the car.

$\frac{km}{h}$

Answer:_______________

Town A and Town B were 836 km apart. At 1045 h Pavi drove from Town A to Town B. At the same time, Prem drove from Town B to Town A on the same road. Both of them did not change their speeds throughout their journeys. Pavi and Prem passed each other at 1530 h. If Pavi was travelling 30 $\frac{km}{h}$ slower than Prem, find Prem's speed.

$\frac{km}{h}$

Answer:_______________

Town Lala and Town Yaya are 650 km apart. At 8.30 a.m., a car left Town Lala for Town Yaya, travelling at a constant speed. At the same time, a lorry set off from Town Yaya for Town Lala at a constant speed too. At 1.30 p.m.,the two vehicles passed each other. If the speed of the car was 20 $\frac{km}{h}$ faster than the lorry, find the speed of the car.

$\frac{km}{h}$

Answer:_______________

Town A and Town B were 798 km apart. At 1045 h Nandini drove from Town A to Town B. At the same time, Murugan drove from Town B to Town A on the same road. Both of them did not change their speeds throughout their journeys. Nandini and Murugan passed each other at 1530 h. If Nandini was travelling 26 $\frac{km}{h}$ slower than Murugan, find Murugan's speed.

$\frac{km}{h}$

Answer:_______________

Town Lala and Town Yaya are 690 km apart. At 8.30 a.m., a car left Town Lala for Town Yaya, travelling at a constant speed. At the same time, a lorry set off from Town Yaya for Town Lala at a constant speed too. At 1.30 p.m.,the two vehicles passed each other. If the speed of the car was 30 $\frac{km}{h}$ faster than the lorry, find the speed of the car.

$\frac{km}{h}$

Answer:_______________

Town A and Town B were 912 km apart. At 1045 h Ramani drove from Town A to Town B. At the same time, Prem drove from Town B to Town A on the same road. Both of them did not change their speeds throughout their journeys. Ramani and Prem passed each other at 1530 h. If Ramani was travelling 10 $\frac{km}{h}$ slower than Prem, find Prem's speed.

$\frac{km}{h}$

Answer:_______________

Town Lala and Town Yaya are 690 km apart. At 8.30 a.m., a car left Town Lala for Town Yaya, travelling at a constant speed. At the same time, a lorry set off from Town Yaya for Town Lala at a constant speed too. At 1.30 p.m.,the two vehicles passed each other. If the speed of the car was 12 $\frac{km}{h}$ faster than the lorry, find the speed of the car.

$\frac{km}{h}$

Answer:_______________

Town A and Town B were 950 km apart. At 1045 h Pavi drove from Town A to Town B. At the same time, Raj drove from Town B to Town A on the same road. Both of them did not change their speeds throughout their journeys. Pavi and Raj passed each other at 1530 h. If Pavi was travelling 14 $\frac{km}{h}$ slower than Raj, find Raj's speed.

$\frac{km}{h}$

Answer:_______________

Town Lala and Town Yaya are 660 km apart. At 8.30 a.m., a car left Town Lala for Town Yaya, travelling at a constant speed. At the same time, a lorry set off from Town Yaya for Town Lala at a constant speed too. At 1.30 p.m.,the two vehicles passed each other. If the speed of the car was 10 $\frac{km}{h}$ faster than the lorry, find the speed of the car.

$\frac{km}{h}$

Answer:_______________

10)

Town A and Town B were 912 km apart. At 1045 h Selvanayaki drove from Town A to Town B. At the same time, Aravindh drove from Town B to Town A on the same road. Both of them did not change their speeds throughout their journeys. Selvanayaki and Aravindh passed each other at 1530 h. If Selvanayaki was travelling 18 $\frac{km}{h}$ slower than Aravindh, find Aravindh's speed.

$\frac{km}{h}$

Answer:_______________

Answer: 78 $\frac{km}{h}$

SOLUTION 1 :

Step 1:	Travelling time	→	1.30 p.m. - 8.30 a.m.
		=	5h

Step 2:	1h	→	12 km
	5h	→	5 x 12 km
		=	60 km

The lorry travelled 60 km less than the car.

Lorry

Car

60km

Total = 720 km

Step 3: 720 km - 60 km = 660 km

Step 4:	Distance travelled by the lorry	→	660 km ÷ 2
		=	330 km

Step 5:	Distance travelled by the car	→	330 km + 60 km
		=	390 km

Step 6:	Car's speed	→	390 km ÷ 5h
		=	78 $\frac{km}{h}$

SOLUTION 2 :

Step 1:	Travelling time	→	1.30 p.m. - 8.30 a.m.
		=	5h

Step 2:	1h	→	12 km
	5h	→	5 x 12 km
		=	60 km

The lorry travelled 60 km less than the car.

Lorry

Car

60km

Total = 720 km

Step 3: 720 km - 60 km = 660 km

Step 4:	Distance travelled by the lorry	→	660 km ÷ 2
		=	330 km

Step 5:	Lorry's speed	→	330 km ÷ 5h
		=	66 $\frac{km}{h}$

Step 6:	Car's speed	→	66 $\frac{km}{h}$ + 12 $\frac{km}{h}$
		=	78 $\frac{km}{h}$

Answer: 103 $\frac{km}{h}$

SOLUTION 1 :

Step 1:	Travelling time	→	1530 h - 1045 h
		=	4 $\frac{3}{4}$ h

Step 2:	1h	→	30 km
	4 $\frac{3}{4}$ h	→	4 $\frac{3}{4}$ x 30 km
		=	142.5 km

Pavi travelled 142.5 km less than Prem.

Pavi

Prem

142.5km

Total = 836 km

Step 3: 836 km - 142.5 km = 693.5 km

Step 4:	Distance travelled by Pavi	→	693.5 km ÷ 2
		=	346.75 km

Step 5:	Pavi's speed	→	346.75 km ÷ 4 $\frac{3}{4}$ h
		=	73 $\frac{km}{h}$

Step 6:	Prem's speed	→	73 $\frac{km}{h}$ + 30 $\frac{km}{h}$
		=	103 $\frac{km}{h}$

SOLUTION 2 :

Step 1:	Travelling time	→	1530 h - 1045 h
		=	4 $\frac{3}{4}$ h

Step 2:	1h	→	30 km
	4 $\frac{3}{4}$ h	→	4 $\frac{3}{4}$ x 30 km
		=	142.5 km

Pavi travelled 142.5 km less than Prem.

Pavi

Prem

142.5km

Total = 836 km

Step 3: 836 km - 142.5 km = 693.5 km

Step 4:	Distance travelled by Pavi	→	693.5 km ÷ 2
		=	346.75 km

Step 5:	Distance travelled by Prem	→	346.75 km + 142.5 km
		=	489.25 km

Step 6:	Prem's speed	→	489.25 km ÷ 4 $\frac{3}{4}$ h
		=	103 $\frac{km}{h}$

Answer: 75 $\frac{km}{h}$

SOLUTION 1 :

Step 1:	Travelling time	→	1.30 p.m. - 8.30 a.m.
		=	5h

Step 2:	1h	→	20 km
	5h	→	5 x 20 km
		=	100 km

The lorry travelled 100 km less than the car.

Lorry

Car

100km

Total = 650 km

Step 3: 650 km - 100 km = 550 km

Step 4:	Distance travelled by the lorry	→	550 km ÷ 2
		=	275 km

Step 5:	Distance travelled by the car	→	275 km + 100 km
		=	375 km

Step 6:	Car's speed	→	375 km ÷ 5h
		=	75 $\frac{km}{h}$

SOLUTION 2 :

Step 1:	Travelling time	→	1.30 p.m. - 8.30 a.m.
		=	5h

Step 2:	1h	→	20 km
	5h	→	5 x 20 km
		=	100 km

The lorry travelled 100 km less than the car.

Lorry

Car

100km

Total = 650 km

Step 3: 650 km - 100 km = 550 km

Step 4:	Distance travelled by the lorry	→	550 km ÷ 2
		=	275 km

Step 5:	Lorry's speed	→	275 km ÷ 5h
		=	55 $\frac{km}{h}$

Step 6:	Car's speed	→	55 $\frac{km}{h}$ + 20 $\frac{km}{h}$
		=	75 $\frac{km}{h}$

Answer: 97 $\frac{km}{h}$

SOLUTION 1 :

Step 1:	Travelling time	→	1530 h - 1045 h
		=	4 $\frac{3}{4}$ h

Step 2:	1h	→	26 km
	4 $\frac{3}{4}$ h	→	4 $\frac{3}{4}$ x 26 km
		=	123.5 km

Nandini travelled 123.5 km less than Murugan.

Nandini

Murugan

123.5km

Total = 798 km

Step 3: 798 km - 123.5 km = 674.5 km

Step 4:	Distance travelled by Nandini	→	674.5 km ÷ 2
		=	337.25 km

Step 5:	Nandini's speed	→	337.25 km ÷ 4 $\frac{3}{4}$ h
		=	71 $\frac{km}{h}$

Step 6:	Murugan's speed	→	71 $\frac{km}{h}$ + 26 $\frac{km}{h}$
		=	97 $\frac{km}{h}$

SOLUTION 2 :

Step 1:	Travelling time	→	1530 h - 1045 h
		=	4 $\frac{3}{4}$ h

Step 2:	1h	→	26 km
	4 $\frac{3}{4}$ h	→	4 $\frac{3}{4}$ x 26 km
		=	123.5 km

Nandini travelled 123.5 km less than Murugan.

Nandini

Murugan

123.5km

Total = 798 km

Step 3: 798 km - 123.5 km = 674.5 km

Step 4:	Distance travelled by Nandini	→	674.5 km ÷ 2
		=	337.25 km

Step 5:	Distance travelled by Murugan	→	337.25 km + 123.5 km
		=	460.75 km

Step 6:	Murugan's speed	→	460.75 km ÷ 4 $\frac{3}{4}$ h
		=	97 $\frac{km}{h}$

Answer: 84 $\frac{km}{h}$

SOLUTION 1 :

Step 1:	Travelling time	→	1.30 p.m. - 8.30 a.m.
		=	5h

Step 2:	1h	→	30 km
	5h	→	5 x 30 km
		=	150 km

The lorry travelled 150 km less than the car.

Lorry

Car

150km

Total = 690 km

Step 3: 690 km - 150 km = 540 km

Step 4:	Distance travelled by the lorry	→	540 km ÷ 2
		=	270 km

Step 5:	Distance travelled by the car	→	270 km + 150 km
		=	420 km

Step 6:	Car's speed	→	420 km ÷ 5h
		=	84 $\frac{km}{h}$

SOLUTION 2 :

Step 1:	Travelling time	→	1.30 p.m. - 8.30 a.m.
		=	5h

Step 2:	1h	→	30 km
	5h	→	5 x 30 km
		=	150 km

The lorry travelled 150 km less than the car.

Lorry

Car

150km

Total = 690 km

Step 3: 690 km - 150 km = 540 km

Step 4:	Distance travelled by the lorry	→	540 km ÷ 2
		=	270 km

Step 5:	Lorry's speed	→	270 km ÷ 5h
		=	54 $\frac{km}{h}$

Step 6:	Car's speed	→	54 $\frac{km}{h}$ + 30 $\frac{km}{h}$
		=	84 $\frac{km}{h}$

Answer: 101 $\frac{km}{h}$

SOLUTION 1 :

Step 1:	Travelling time	→	1530 h - 1045 h
		=	4 $\frac{3}{4}$ h

Step 2:	1h	→	10 km
	4 $\frac{3}{4}$ h	→	4 $\frac{3}{4}$ x 10 km
		=	47.5 km

Ramani travelled 47.5 km less than Prem.

Ramani

Prem

47.5km

Total = 912 km

Step 3: 912 km - 47.5 km = 864.5 km

Step 4:	Distance travelled by Ramani	→	864.5 km ÷ 2
		=	432.25 km

Step 5:	Ramani's speed	→	432.25 km ÷ 4 $\frac{3}{4}$ h
		=	91 $\frac{km}{h}$

Step 6:	Prem's speed	→	91 $\frac{km}{h}$ + 10 $\frac{km}{h}$
		=	101 $\frac{km}{h}$

SOLUTION 2 :

Step 1:	Travelling time	→	1530 h - 1045 h
		=	4 $\frac{3}{4}$ h

Step 2:	1h	→	10 km
	4 $\frac{3}{4}$ h	→	4 $\frac{3}{4}$ x 10 km
		=	47.5 km

Ramani travelled 47.5 km less than Prem.

Ramani

Prem

47.5km

Total = 912 km

Step 3: 912 km - 47.5 km = 864.5 km

Step 4:	Distance travelled by Ramani	→	864.5 km ÷ 2
		=	432.25 km

Step 5:	Distance travelled by Prem	→	432.25 km + 47.5 km
		=	479.75 km

Step 6:	Prem's speed	→	479.75 km ÷ 4 $\frac{3}{4}$ h
		=	101 $\frac{km}{h}$

Town Lala and Town Yaya are 690 km apart. At 8.30 a.m., a car left Town Lala for Town Yaya, travelling at a constant speed. At the same time, a lorry set off from Town Yaya for Town Lala at a constant speed too. At 1.30 p.m.,the two vehicles passed each other. If the speed of the car was 12 $\frac{km}{h}$ faster than the lorry, find the speed of the car.

Answer: 75 $\frac{km}{h}$

SOLUTION 1 :

Step 1:	Travelling time	→	1.30 p.m. - 8.30 a.m.
		=	5h

Step 2:	1h	→	12 km
	5h	→	5 x 12 km
		=	60 km

The lorry travelled 60 km less than the car.

Lorry

Car

60km

Total = 690 km

Step 3: 690 km - 60 km = 630 km

Step 4:	Distance travelled by the lorry	→	630 km ÷ 2
		=	315 km

Step 5:	Distance travelled by the car	→	315 km + 60 km
		=	375 km

Step 6:	Car's speed	→	375 km ÷ 5h
		=	75 $\frac{km}{h}$

SOLUTION 2 :

Step 1:	Travelling time	→	1.30 p.m. - 8.30 a.m.
		=	5h

Step 2:	1h	→	12 km
	5h	→	5 x 12 km
		=	60 km

The lorry travelled 60 km less than the car.

Lorry

Car

60km

Total = 690 km

Step 3: 690 km - 60 km = 630 km

Step 4:	Distance travelled by the lorry	→	630 km ÷ 2
		=	315 km

Step 5:	Lorry's speed	→	315 km ÷ 5h
		=	63 $\frac{km}{h}$

Step 6:	Car's speed	→	63 $\frac{km}{h}$ + 12 $\frac{km}{h}$
		=	75 $\frac{km}{h}$

Answer: 107 $\frac{km}{h}$

SOLUTION 1 :

Step 1:	Travelling time	→	1530 h - 1045 h
		=	4 $\frac{3}{4}$ h

Step 2:	1h	→	14 km
	4 $\frac{3}{4}$ h	→	4 $\frac{3}{4}$ x 14 km
		=	66.5 km

Pavi travelled 66.5 km less than Raj.

Pavi

Raj

66.5km

Total = 950 km

Step 3: 950 km - 66.5 km = 883.5 km

Step 4:	Distance travelled by Pavi	→	883.5 km ÷ 2
		=	441.75 km

Step 5:	Pavi's speed	→	441.75 km ÷ 4 $\frac{3}{4}$ h
		=	93 $\frac{km}{h}$

Step 6:	Raj's speed	→	93 $\frac{km}{h}$ + 14 $\frac{km}{h}$
		=	107 $\frac{km}{h}$

SOLUTION 2 :

Step 1:	Travelling time	→	1530 h - 1045 h
		=	4 $\frac{3}{4}$ h

Step 2:	1h	→	14 km
	4 $\frac{3}{4}$ h	→	4 $\frac{3}{4}$ x 14 km
		=	66.5 km

Pavi travelled 66.5 km less than Raj.

Pavi

Raj

66.5km

Total = 950 km

Step 3: 950 km - 66.5 km = 883.5 km

Step 4:	Distance travelled by Pavi	→	883.5 km ÷ 2
		=	441.75 km

Step 5:	Distance travelled by Raj	→	441.75 km + 66.5 km
		=	508.25 km

Step 6:	Raj's speed	→	508.25 km ÷ 4 $\frac{3}{4}$ h
		=	107 $\frac{km}{h}$

Answer: 71 $\frac{km}{h}$

SOLUTION 1 :

Step 1:	Travelling time	→	1.30 p.m. - 8.30 a.m.
		=	5h

Step 2:	1h	→	10 km
	5h	→	5 x 10 km
		=	50 km

The lorry travelled 50 km less than the car.

Lorry

Car

50km

Total = 660 km

Step 3: 660 km - 50 km = 610 km

Step 4:	Distance travelled by the lorry	→	610 km ÷ 2
		=	305 km

Step 5:	Distance travelled by the car	→	305 km + 50 km
		=	355 km

Step 6:	Car's speed	→	355 km ÷ 5h
		=	71 $\frac{km}{h}$

SOLUTION 2 :

Step 1:	Travelling time	→	1.30 p.m. - 8.30 a.m.
		=	5h

Step 2:	1h	→	10 km
	5h	→	5 x 10 km
		=	50 km

The lorry travelled 50 km less than the car.

Lorry

Car

50km

Total = 660 km

Step 3: 660 km - 50 km = 610 km

Step 4:	Distance travelled by the lorry	→	610 km ÷ 2
		=	305 km

Step 5:	Lorry's speed	→	305 km ÷ 5h
		=	61 $\frac{km}{h}$

Step 6:	Car's speed	→	61 $\frac{km}{h}$ + 10 $\frac{km}{h}$
		=	71 $\frac{km}{h}$

10)

Answer: 105 $\frac{km}{h}$

SOLUTION 1 :

Step 1:	Travelling time	→	1530 h - 1045 h
		=	4 $\frac{3}{4}$ h

Step 2:	1h	→	18 km
	4 $\frac{3}{4}$ h	→	4 $\frac{3}{4}$ x 18 km
		=	85.5 km

Selvanayaki travelled 85.5 km less than Aravindh.

Selvanayaki

Aravindh

85.5km

Total = 912 km

Step 3: 912 km - 85.5 km = 826.5 km

Step 4:	Distance travelled by Selvanayaki	→	826.5 km ÷ 2
		=	413.25 km

Step 5:	Selvanayaki's speed	→	413.25 km ÷ 4 $\frac{3}{4}$ h
		=	87 $\frac{km}{h}$

Step 6:	Aravindh's speed	→	87 $\frac{km}{h}$ + 18 $\frac{km}{h}$
		=	105 $\frac{km}{h}$

SOLUTION 2 :

Step 1:	Travelling time	→	1530 h - 1045 h
		=	4 $\frac{3}{4}$ h

Step 2:	1h	→	18 km
	4 $\frac{3}{4}$ h	→	4 $\frac{3}{4}$ x 18 km
		=	85.5 km

Selvanayaki travelled 85.5 km less than Aravindh.

Selvanayaki

Aravindh

85.5km

Total = 912 km

Step 3: 912 km - 85.5 km = 826.5 km

Step 4:	Distance travelled by Selvanayaki	→	826.5 km ÷ 2
		=	413.25 km

Step 5:	Distance travelled by Aravindh	→	413.25 km + 85.5 km
		=	498.75 km

Step 6:	Aravindh's speed	→	498.75 km ÷ 4 $\frac{3}{4}$ h
		=	105 $\frac{km}{h}$