Ncert exemplar solutions mathematics class 8 Solutions for Chapter 10 direct and inverse proportions

Both u and v vary directly with each other. When u is 10, v is 15, which of the following is not a possible pair of corresponding values of u and v?

(a) 2 and 3

(b) 8 and 12

(c) 15 and 20

(d) 25 and 37.5

Assuming land to be uniformly fertile, the area of land and the yield on it vary

(a) directly with each other.

(b) inversely with each other.

(c) neither directly nor inversely with each other.

(d) sometimes directly and sometimes inversely with each other.

The number of teeth and the age of a person vary

(a) directly with each other.

(b) inversely with each other.

(c) neither directly nor inversely with each other.

(d) sometimes directly and sometimes inversely with each other

A truck needs 54 litres of diesel for covering a distance of 297 km. The diesel required by the truck to cover a distance of 550 km is

(a) 100 litres

(b) 50 litres

(c) 25.16 litres

(d) 25 litres

In which of the following case, do the quantities vary directly with each other?

(a)

(b)

(c)

(d)

Which quantities in the previous question vary inversely with each other?

(a) x and y

(b) p and q

(c) r and s

(d) u and v

Which of the following vary inversely with each other?

(a) speed and distance covered.

(b) distance covered and taxi fare.

(c) distance travelled and time taken.

(d) speed and time taken.

Both x and y are in direct proportion, then 1/x and 1/y are:

(a) in indirect proportion.

(b) in inverse proportion.

(c) neither in direct nor in inverse proportion.

(d) sometimes in direct and sometimes in inverse proportion.

Meenakshee cycles to her school at an average speed of 12 km/h and takes 20 minutes to reach her school. If she wants to reach her school in 12 minutes, her average speed should be

(a) 20/3 km/h

(b) 16 km/h

(c) 20 km/h

(d) 15 km/h

100 persons had food provision for 24 days. If 20 persons left the place, the provision will last for

(a) 30 days

(b) 96/5 days

(c) 120 days

(d) 40 days

If two quantities x and y vary directly with each other, then

(a) x/y remains constant.

(b) x – y remains constant.

(c) x + y remains constant.

(d) x × y remains

constant.

If two quantities p and q vary inversely with each other, then:

(a) p/q remains constant.

(b) p + q remains constant.

(c) p × q remains constant.

(d) p – q remains

constant.

If the distance travelled by a rickshaw in one hour is 10 km, then the distance travelled by the same rickshaw with the same speed in one minute is:

(a) 250/9 m (b) 500/9 m (c) 1000 m (d) 500/3 m

Both x and y vary directly with each other and when x is 10, y is 14, which of the following is not a possible pair of corresponding values of x and y?

(a) 25 and 35 (b) 35 and 25 (c) 35 and 49 (d) 15 and 21

If x = 5y, then x and y vary ________ with each other.

If xy = 10, then x and y vary __________ with each other.

When two quantities x and y are in _________ proportion or vary _________ they are written as x ∝ y.

When two quantities x and y are in ________ proportion or vary ___________ they are written as x ∝ 1/y.

Both x and y are said to vary __________ with each other if for some positive number k, xy = k.

x and y are said to vary directly with each other if for some positive number k, _______ =k.

Two quantities are said to vary ___________ with each other if they increase (decrease) together in such a manner that the ratio of their corresponding values remains constant.

Two quantities are said to vary _______ with each other if an increase in one causes a decrease in the other in such a manner that the product of their corresponding values remains constant.

If 12 pumps can empty a reservoir in 20 hours, then time required by 45 such pumps to empty the same reservoir is ______ hours.

If x varies inversely as y, then

If x varies directly as y, then

When the speed remains constant, the distance travelled is ________ proportional to the time.

On increasing a, b increases in such a manner that a/b remains _________ and positive, then a and b are said to vary directly with each other.

If on increasing a, b decreases in such a manner that ______ remains _______ and positive, then a and b are said to vary inversely with each other.

If two quantities x and y vary directly with each other, then _______ of their corresponding values remains constant.

If two quantities p and q vary inversely with each other then _______ of their corresponding values remains constant.

The perimeter of a circle and its diameter vary ________ with each other.

A car is travelling 48 km in one hour. The distance travelled by the car in 12 minutes is _______ .

An auto rickshaw takes 3 hours to cover a distance of 36 km. If its speed is increased by 4 km/h, the time taken by it to cover the same distance is __________.

If the thickness of a pile of 12 cardboard sheets is 45 mm, then the thickness of a pile of 240 sheets is _______ cm.

If x varies inversely as y and x = 4 when y = 6, then when x = 3 the value of y is _______.

In direct proportion, a1/b1 = a2/b2

In case of inverse proportion, a2/a1= ______

If the area occupied by 15 postal stamps is 60 cm2, then the area occupied by 120 such postal stamps will be _______.

If 45 persons can complete a work in 20 days, then the time taken by 75 persons will be ______ hours.

Devangi travels 50 m distance in 75 steps, then the distance travelled in 375 steps is _______ km.

Two quantities x and y are said to vary directly with each other if for some rational number k, xy = k.

When the speed is kept fixed, time and distance vary inversely with each other.

When the distance is kept fixed, speed and time vary directly with each other.

Length of a side of a square and its area vary directly with each other.

Length of a side of an equilateral triangle and its perimeter vary inversely with each other.

If d varies directly as t2, then we can write dt2 = k, where k is some constant.

If a tree 24 m high casts a shadow of 15 m, then the height of a pole that casts a shadow of 6 m under similar conditions is 9.6 m.

If x and y are in direct proportion, then (x – 1) and (y – 1) are also in direct proportion.