Maths - Simplification & Time and Distance!!!

Simplification

70% of 1680 + ?% of 1750 = 55% of 2820 – 886

(70/100) × 1680 + (?/100) × 1750 = 

(55/100) × 2820 – 886

1176 + (?/10) × 175 = 1551 – 886 = 665

(?/10) × 175 = 665 – 1176 = – 511

? = {(–511 × 10) /175} = 29.2

√196 × √144 × 20% of 500 = ? + 1256

√196 × √144 × 20% of 500 = ? + 1256

⇒ 14 × 12 ×	20	× 500 = ? + 1256
	100

⇒ 168 × 100 = ? + 1256

⇒ 16800 = ? + 1256

⇒ ? =16800 – 1256

⇒ ? = 15,544

(17)2 + 6 × (13)2 – 212 × 6 = ?

(17)2 + 6 × (13)2 – 212 × 6 = ?

 

? = 289 + 1014 – 1272

 

? = 1303 – 1272

? = 31

235.265 – 483.67 + 956.71 + 33.523 – 17.231 = ?

235.265 – 483.67 + 956.71 + 33.523 – 17.231 = ?

 

? = 1225.498 – 500.901

 

? = 724.597

25% of 680 + 16% of 525 – 22% of 450 = ?

25% of 680 + 16% of 525 – 22% of 450 = ?

 

? = 170 + 84 – 99

 

? = 155

Time and Distance

A man starts from a place P and reaches the place Q in 7 hours. He travels 1/4 th of the distance at 10 km/hour and the remaining distance at 12 km/hour. The distance, in kilometer, between P and Q is:

Let one-fourth of the distance between P and Q be x km

then

Time taken for the first one-fourth distance =	x	km/hour
	10

and

Time taken for the remaining distance =	3x	km/hour
	12

Since  Total time taken is 7 hours.

⇒ 7 =	x	+	3x
	10		12

On solving, x = 20

Total distance = 4x = 80 km.

In the school, Mohan and Govind took a part in the race and the ratio between their speeds is 5 : 7. Mohan losses the race by 360m then what is the length of the track (in km)?

t =	D
	S

According to the question,

Let Speed = 5x, 7x Distance = y m

y – 360	=	y
5x		7x

y – 360	=	y
5		7

7 (y – 360) = 5y

7y – 5y = 2520

2y = 2520

y = 1260

= 1.26 km.

The respective ratio between the speed of a car, a train, and a bus is 5 : 9 : 4.The average speed of the car , the bus and the train is 72 km/hr together. What is the average speed of the car and the train together?

Let speed of the car, the train, and the bus be 5a Km/hr , 9a Km/hr and 4a Km/hr respectively
 

Given   

total speed = (72 × 3) Km/hr  = 216 Km/hr
 

⇒    5a + 9a + 4a = 216
 

⇒    18a = 216
 

⇒    a = 12Km/hr 
 

⇒    speed of car = 5 × 12 = 60 Km/hr
 

And     

speed of train = 9 × 12 = 108 Km/hr

 

⇒ their average speed =	60 + 108	= 84 Km/hr
	2

Mohit and Anuj took a part in a race. Mohit runs 300m in 50 second and Anuj takes 1 minute to cover the same distance. By what distance will Mohit beat Anuj in 300 m race?

Mohit runs 300m in 50 sec.

 

Anuj runs 300m in 60 sec.

Now, In 1 sec Anuj runs 5m

Therefore, in 50 sec Anuj runs 50×5 = 250m
 
Mohit beats Anuj by 300 - 250 = 50m .

A beats B by 15 sec in a 200 m race, B beats C by 25 sec in a 500 m race, C beats D by 32 sec in  800 m race and D beats E by 35 sec in a 1 km race. What must be the speed of A in order to beat E by 800 m in a 2 km race? 

A beats B by 15 sec means A reaches the destination 15 sec ahead of B or B reaches 15 sec later than B.  Let all of them compete in a 2 km  or 2000 m race, now we can compare them as follows:
 

A beats B by 150 sec, B beats C by 100 sec, C beats D by 80 sec, D beats E by 70 sec, ⇒ E would finish the race 400 sec after A.
 

Now, if A has to beat E by 800 m then we can say that E will cover the remaining 800m in 400sec, and cover 2000m in 1000 sec. A has to reach 400s earlier i.e in 600 sec, 
 

so A’s speed =	2000	= 3.33 m/s.
	600

A person travelled 132 km by auto, 852 km by train and 248 km by bike. It took 21 hours in all. If the speed of train is 6 times the speed of auto and 1.5 times speed of bike, what is the speed of train?

Let the speed of auto be x kmph-1 . So, the speed of train will be 6x and that of bike will be

=	6 x	= 4x
	1.5

As per the given information,

Time taken by auto + Time taken by train + Time taken by bike = 21 hours
 

⇒	132	+	852	+	248	= 21
	x		6x		4x

or,	132	+	142	+	62	= 21
	x		x		x

or,  21x = 132 + 142 + 62 = 336
 

∴   x =	336	= 16
	21

∴   Speed of the train = 6x =  6 × 16 = 96 kmh-1

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