Word Problems: Power Play | Mathematics Class 8- New NCERT (Ganita Prakash) PDF Download

Q1: A new sapling starts with a height of 2 cm. How tall might the plant be after 4 years if its height doubles each year?

Solution: Initial height = 2 cm

The height doubles each year, so after 4 years:
= 2¹ × 2⁴
= (2)¹⁺⁴
= 32 cm

The plant will be 32 cm tall after 4 years.

Q2: The number of books in a library increases by 5 times every 2 years. A library starts with 100 books. How many books will there be in the library after:

(a) 6 years

(b) 10 years

Solution:  Initial number of books = 100

The number of books increases by a factor of 5 every 2 years.

(a) After 6 years (3 periods of 2 years):

Number of books after 6 years = 100 × 5³ = 100 × 125 = 12500 books

• After 6 years: 12500 books

(b) After 10 years (5 periods of 2 years):

Number of books after 10 years = 100 × 5⁵ = 100 × 3125 = 312500 books

• After 10 years: 312500 books

Q3: The number of bacteria in a culture increases 3 times every hour. A culture starts with 1 bacterium. How many bacteria will be in the culture after 5 hours?

Solution:

Initial bacteria = 1

The bacteria triple every hour, so after 5 hours:
Number of bacteria after 5 hours = 1 × 3⁵ = 1 × 243 = 243 bacteria

The number of bacteria will be 243 after 5 hours.

Q4: The planet Uranus is approximately 2,896,819,200,000 metres awayfrom the Sun. What is this distance in standard form?

Solution:

The distance of Uranus from the Sun is given as 2,896,819,200,000 meters.

To express this in standard form:

2,896,819,200,000 = 2.8968192 × 10¹²

So, the distance of Uranus from the Sun in standard form is:

2.8968192 × 10¹² meters

Q5: An inch is approximately equal to 0.02543 metres. Write this distance in standard form.

Solution:

We are given that 1 inch ≈ 0.02543 meters.

To express this in standard form:

0.02543 = 2.543 × 10⁻²

So, the distance in standard form is:

2.543 × 10⁻² meters

Q6: A particular star is at a distance of about 8.1 × 10¹³ km from the Earth. Assuring that light travels at 3 × 10⁸ m per second, find how long does light takes from that star to reach the Earth.

Solution:

Given, a particular star is at a distance of about 8.1 × 10¹³ km from the Earth.

Assuring that light travels at 3 × 10⁸ m per second.

We have to find the time the light takes from that star to reach the Earth.

We know, speed = distance / time

Given, speed = 3 × 10⁸ m/s

Distance = 8.1 × 10¹³ km

We know, 1 km = 1000 m

= 8.1 × 10¹³ × 10³

Using the law of exponents,

a^m × aⁿ = a^{m + n}

= 8.1 × 10^{13 + 3}

= 8.1 × 10¹⁶ m

Time = distance / speed

= 8.1 × 10¹⁶ / 3 × 10⁸

= (8.1 / 3) × (10¹⁶/10⁸)

= 2.7 × (10¹⁶/10⁸)

Using the law of exponents,

a^m ÷ aⁿ = a^{m - n}

= 2.7 × 10^{16 - 8}

= 2.7 × 10⁸ seconds

Therefore, the required time is 2.7 × 10⁸ seconds.

Q7: In a stack, there are 4 books, each of thickness 15mm, and 6 paper sheets, each of thickness 0.010mm. What is the total thickness of the stack?

Solution:

Thickness of each book = 15mm

Number of books in the stack = 4

Thickness of 4 books = 4 × 15 = 60mm

Thickness of each paper sheet = 0.010mm

Thickness of 6 paper sheets = 6 × 0.010 = 0.060mm

Total thickness of the stack = 60mm + 0.060mm = 60.060mm

Q8: A number when divides ( –15) ^–1 results ( –5) ^–1. Find the number.

Solution:

Let x be the number such that

( –15) ^–1 ÷ x = ( –5) ^–1

⇒ –1/15 ÷ x = –⅕

⇒ –1/15 × 1/x = –⅕

⇒ –1/15x = –⅕

⇒ 15x = 5

⇒ x = ⅓ or 3 ^–1

Q9: A savings account balance quadruples every 3 years. The initial balance in a savings account is 1500 rupees. How much will the balance be after 9 years?

Solution:

​Initial balance = 1500 rupees

The balance quadruples every 3 years, so after 9 years:

Balance after 9 years = 1500 × 4³ = 1500 × 64 = 96000 rupees

The balance will be 96000 rupees after 9 years

Q10: The volume of the Earth is approximately 7.67 × 10^–7 times thevolume of the Sun. Express this figure in usual form.

Solution:

The volume of Earth is approximately 7.67 × 10^–7 times the volume of the Sun. We are asked to express this in usual form.

To convert from scientific notation to usual form, we move the decimal point to the left by 7 places (since the exponent is -7):

7.67 × 10^–7 = 0.000000767

So, the volume of Earth as a fraction of the volume of the Sun is:

0.000000767