Advertisements
Advertisements
प्रश्न
From the same place at 7 a.m. A started walking in the north at a speed of 4 km/hr. after 1 hour, B started cycling in the east at a speed of 8 km/hr. at what time will they be at a distance of 20 km apart from each other?
उत्तर
Let t = travel time of bicycle
then (t + 1) = Walking time
Distance = Speed × Time
This is a Pythagoras problem
`a^2 + b^2 = c^2`
Where a = 8t, bicycle distance
b = 4(t + 1), walking distance
c = 20, distnace apart in t hrs from 8 a.m.
∴ `(8t)^2 + [4(t + 1)]^2 = (20)^2`
`64t^2 + 16(t^2 + 1 + 2t) = 400`
`64t^2 + 16t^2 + 32t + 16 = 400`
`80t^2 + 32t - 384 = 0`
`16(5t^2 + 2t - 24) = 0`
`5t^2 + 2t - 24 = 0`
`5t^2 + (12 - 10) t - 24 = 0`
`5t^2 + 12t - 10 t - 24 = 0`
`5t^2 - 10t + 12 t - 2 4 = 0`
`5t(t - 2) + 12(t - 2) = 0`
`(t -2)(5t + 12) = 0`
t = 2
and `t = -12/15`which is not possible
Positive solution t = 2 hrs.
At 10 a.m. they will be 20 km apart.
APPEARS IN
संबंधित प्रश्न
There are three boys and two girls. A committee of two is to be formed. Find the probability of the following events:
Event A: The committee contains at least one girl
Event B: The committee contains one boy and one girl
A game of chance consists of spinning an arrow on a circular board, divided into 8 equal parts, which comes to rest pointing at one of the numbers 1, 2, 3, ..., 8 (Fig. 9), which are equally likely outcomes. What is the probability that the arrow will point at (i) an odd number (ii) a number greater than 3 (iii) a number less than 9.
Two dice are thrown. Find the probability of the event that the product of numbers on their upper faces is 12.
An integer is chosen at random between 1 and 100. Find the probability that it is
1) divisible by 8.
2) not divisible by 8.
In the Fig. below, JKLM is a square with sides of length 6 units. Points A and B are the
mid- points of sides KL and LM respectively. If a point is selected at random from the
interior of the square. What is the probability that the point will be chosen from the interior of ΔJAB?
A bag contains 3 red balls and 5 black balls. A ball is draw at random from the bag. What is the probability that the ball drawn is not red?
A box contains 5 red marbles, 8 white marbles, and 4 green marbles, One marble is taken out of the box at random. What is the probability that the marble taken out will be red?
A bag contains cards numbered from 1 to 49. A card is drawn from the bag at random, after mixing the card thoroughly. Find the probability that the number on the drawn card is an odd number
Suppose you drop a tie at random on the rectangular region shown in the given figure. What is the probability that it will land inside the circle with diameter 1 m?
Two coins are tossed simultaneously. What is the probability of getting at least one head?
A month is selected at random in a year. The probability that it is March or October, is
If a two digit number is chosen at random, then the probability that the number chosen is a multiple of 3, is
A box contains 25 cards numbered from 1 to 25. A card is drawn at random from the bag. Find the probability that the number on the drawn card is divisible by 2 or 3.
A carton consists of 100 shirts of which 88 are good and 8 have minor defects. Rohit, a trader, will only accept the shirts which are good. But Kamal, an another trader, will only reject the shirts which have major defects. One shirt is drawn at random from the carton. What is the probability that it is acceptable to Kamal?
Two coins are tossed together . what is the probabilty of getting different faces on the coins ?
A box contains a certain number of balls. Some of these balls are marked A, some are marked B and the remaining are marked C. When a ball is drawn at random from the box P(A) = `1/3` and P(B) = `1/4`. If there are 40 balls in the box which are marked C, find the number of balls in the box.
Students of a school were made to stand in rows for drill. If 3 students less were standing in each row, 10 more rows would be required and if 5 students more were standing in each row, then the number of rows would be reduced by 10. Find the number of students participating in the drill.
If A = {1, 2, 3, 4, 5} and B = {1, 3, 7}, then A ∩ B = ?
A die is thrown once. Find the probability of getting a number which
lies between 2 and 6.
What is the probability of throwing an even number with a single standard dice of six faces?
