Selina Solutions Concise Maths Class 10 Chapter 10 Arithmetic Progression
Selina Solutions Concise Maths Class 10 Chapter 10 Arithmetic Progression Exercise 10(E)
Exercise 10(E) Page No: 147
Question 1. Two cars start together in the same direction from the same place. The first car goes at uniform speed of 10 km h-1. The second car goes at a speed of 8 km h-1 in the first hour and thereafter increasing the speed by 0.5 km h-1 each succeeding hour. After how many hours will the two cars meet?
Let’s assume the two cars meet after n hours.
Then, this means that two cars travel the same distance in n hours.
So,
Distance travelled by the 1st car in n hours = 10 x n km
Distance travelled by the 2nd car in n hours = n/2[2×8 + (n – 1) x 0.5] km
10n = n/2[2×8 + (n – 1) x 0.5]
20 = [16 + 0.5n – 0.5]
20 = 15.5 + 0.5n
4.5 = 0.5n
n = 9
Hence, the two cars will meet after 9 hours.
Question 2. A sum of Rs. 700 is to be paid to give seven cash prizes to the students of a school for their overall academic performance. If the cost of each prize is Rs. 20 less than its preceding prize; find the value of each of the prizes.
From the question, it’s understood that
n = 7
d = -20
S7 = 700
We know that,
Sn = n/2[2a + (n – 1)d]
700 = 7/2[2a + (7 -1)(-20)]
200 = [2a + (7 -1)(-20)]
200 = 2a – 120
2a = 320
a = 160
Hence, the value of each prize will be
1st prize – Rs 160, 2nd prize – Rs 140, 3rd prize – Rs 120, 4th prize – Rs 100, 5th prize – Rs 80, 6th prize – Rs 60 and 7th prize – Rs 40
0 Comments
Please Comment