## RS Aggarwal Solutions Class 10 Chapter 10 Quadratic Equations 10D

These Solutions are part of RS Aggarwal Solutions Class 10. Here we have given RS Aggarwal Solutions Class 10 Chapter 10 Quadratic Equations 10D

**Other Exercises**

- RS Aggarwal Solutions Class 10 Chapter 10 Quadratic Equations 10A
- RS Aggarwal Solutions Class 10 Chapter 10 Quadratic Equations 10B
- RS Aggarwal Solutions Class 10 Chapter 10 Quadratic Equations 10C
- RS Aggarwal Solutions Class 10 Chapter 10 Quadratic Equations 10D

**Exercise 10D**

**Question 1:**

Let two numbers be x and 8 – x

Sum of their reciprocals =

Thus, two numbers are 3 and 5.

**More Resources**

**Question 2:**

Let the two numbers are x and x + 4

Difference of their reciprocals =

Hence, the two required numbers are 3 and 7.

**Question 3:**

Let the required number be x and (18- x)

x = 12, x = 6

hence, the required numbers are 12 and 6.

Solving A Quadratic Equation By Completing The Square

**Question 4:**

Let the number be x and y

x – y = 5 —–(1)

Difference of reciprocal

Hence, the two numbers are 10 and 5.

**Question 5:**

Let the number be x

Hence, the required number is

**Question 6:**

Let the required number be x and (57 – x), then

The required numbers are 34 and 23.

**Question 7:**

Let the required number be 3x and 3(x + 1).

**Question 8:**

Let the required consecutive positive even integer be 2x and (2x + 2), then

But -7 is not an even positive integer

Hence, the required integers are 12 and 14.

**Question 9:**

Let the required number be x

**Question 10:**

Let the required number be x, then

**Question 11:**

Let the required number be x and x – 3, then

Hence, the required numbers are (24,21) or (-21 and-24).

**Question 12:**

Let the two consecutive positive integers be x, x + 1

But, -14 is not a positive integer

Hence, the required numbers are 13, 14.

**Question 13:**

Let x, y be the two natural numbers and x > y

∴ ——(1)

Also, square of smaller number = 4 × larger number

⇒ ———(2)

Putting y^{2} value of from (1), we get

Thus, the two required numbers are 9 and 6.

**Question 14:**

Let the required number be x and y, hen

**Question 15:**

Let the smaller part and larger part be x, 16 – x

Then,

-42 is not a positive part

Hence, the larger and smaller parts are 10, 6 respectively.

**Question 16:**

Let the numerator and denominator be x, x + 3

Then,

Hence, numerator and denominator are 2 and 5 respectively and fraction is

**Question 17:**

Let the tens digit be x and units digit be y

Hence, the tens digit is 3 and units digit is (2 × 3)

Hence the required number is 36.

**Question 18:**

Let the tens digit and units digits of the required number be x and y respectively.

The ten digit is 2 and unit digit is 7.

Hence, the required number is 27.

**Question 19:**

Let the total number of birds be x^{2} , then

(∵ number of birds cannot be negative)

Hence, the number of birds = (24)^{2} = 576

**Question 20:**

Let there be x rows and number of student in each row be x

Then, total number of students =

Hence total number of student

= [(24)^{2} + 24] = 576 + 24 = 600

Total number of students is 600.

**Question 21:**

Let the number of students be x, then

(∵ number of birds cannot be negative)

Hence the number of students is 50.

**Question 22:**

Let the number of pens be x

Total cost of the pens is Rs. 80

∴ Cost of one pen = Rs

If the number of pens is increased x + 4

Cost of one pen = Rs

Difference between them = Re 1

Hence, number of pens is 16.

**Question 23:**

Let the marks obtained by Kamal in Mathematics and English be x and y

The marks obtained by Kamal in Mathematics and English respectively are (21,19) or (12,28).

**Question 24:**

Let A and B take x days and x + 10 respectively to finish a piece of work

Work done by A and B in 1 day =

Then, B will finish work in x + 10 days = 20 + 10 = 30 days

**Question 25:**

Let x kmph be the speed of the passenger train

time taken to move 300 km = hours

When speed is (x + 5) km/h, time taken to move 300 km = hours

Speed of passenger train is 25km/h.

**Question 26:**

Let the original speed of the train be x km/h

Then, increased speed = (x + 5) km/h

Time taken at original speed =

Time taken at increased speed =

Then original speed is 40 km/h.

**Question 27:**

Let the original speed of the train be x km.hour

Then speed increases by 15 km/ph = (x + 15)km/hours

Then time taken at original speed = hours

Then, time taken at in increased speed = hours

Difference between the two lines taken h

Then, original speed of the train = 45km / h.

**Question 28:**

Let the speed of the Deccan Queen = x kmph

The, speed of other train = (x – 20)kmph

Then, time taken by Deccan Queen = hours

Time taken by other train = hours

Difference of time taken by two trains is

Hence, speed of Deccan Queen = 80km/h.

**Question 29:**

Let the speed of the stream be = x km/h

Speed of boat in still waters = 9 km/h

Speed of boat down stream = 9 + x

time taken by boat to go 15 km downstream = hours

Speed of boat upstream = 9 – x

time taken by boat to go 15 km of stream = hours

**Question 30:**

Let the speed of stream be x km/h

Speed of boat in still stream = 18 km/h

Speed of boat up the stream = 18 – x km/h

Time taken by boat to go up the stream 24 km = hours

Time taken by boat to go down the stream = hours

Time taken by the boat to go up the stream is 1 hour more that the time taken down the stream

Speed of the stream = 6 km/h.

**Question 31:**

Let the speed of the stream be x kmph

Then the speed of boat down stream = (8 + x) kmph

And the speed of boat upstream = (8 – x)kmph

Time taken to cover 15 km upstream = hours

Time taken to cover 22 km downstream = hours

Total time taken = 5 hours

Hence, the speed of stream is 3 kmph.

**Question 32:**

Let the speed of the boat in still water be x kmph, then

Speed of boat downstream = (x + 2)km/h

And the speed of boat upstream = (x – 2)kmph

Time taken to cover 8 km downstream = hours

Time taken to cover 8 km upstream = hours

Total time taken = hours

Then speed of the boat in still water is 10 kmph.

**Question 33:**

Let the faster pipe takes x minutes to fill the cistern

Then, the other pipe takes (x + 3) minute

The faster pipe takes 5 minutes to fill the cistern

Then, the other pipe takes (5 + 3) minutes = 8 minutes

**Question 34:**

Let the age of son be x and age of man = y

1 year ago

**Question 35:**

Let the age of man and son be x and y

Then, x + y = 45

Five years ago

Product of their ages = 4 times the age of man five years ago

(x – 5)(y – 5) = 4(x – 5)

⇒ y – 5 = 4

y = 9

⇒ x + 9 = 45

x = 45 – 9 = 36

Hence the ages of man and son are 36 years and 9 years respectively.

**Question 36:**

Let the present age of Meena be x

Then,

Hence the present age of Meena is 7 years.

**Question 37:**

Let the ages of two brothers be x and 25 – x

Then,

Hence, present ages of the two brothers is 18 years and 7 years.

**Question 38:**

Let the width of the path be x meters,

Then,

Area of path = 16 × 10 – (16 – 2x) (10 – 2x) = 120

Hence the required width is 3 meter as x cannot be 10m.

**Question 39:**

Let the breadth of a rectangle = x cm

Then, length of the rectangle = 2x cm

Thus, breadth of rectangle = 12 cm

And length of rectangle = (2 × 12) = 24 cm

**Question 40:**

Let the breadth of a rectangle = x meter

Then, length of rectangle = 3x meter

Thus, breadth of rectangle = 7 m

And length of rectangle = (3 × 7)m = 21 m

**Question 41:**

Let the breadth of hall = x meters

Then, length of the hall = (x + 3) meters

Area = length × breadth = 238 m^{2}

Thus, the breadth of hall is 14 cm

And length of the hall is (14 + 3) = 17 cm

**Question 42:**

Let the breadth of the rectangular plot be x meter

Then, Perimeter = 2(length + breadth) = 62 m

⇒ length + breadth = 31m

⇒ length = (31 – x) meters

Area = (31 – x)x sq. meter

Hence the length and breadth of rectangle is 19 m and 12 m.

**Question 43:**

Let the side of square be x cm

Then, length of the rectangle = 3x cm

Breadth of the rectangle = (x – 4) cm

Area of rectangle = Area of square x

Thus, side of the square = 6 cm

And length of the rectangle = (3 × 6) = 18 cm

Then, breadth of the rectangle = (6 – 4) cm = 2 cm

**Question 44:**

Let the length = x meter

Area = length × breadth = 180 m^{2}

If ength of the rectangle = 15 m

Also, if length of rectangle = 24 m

**Question 45:**

Let the altitude of triangle be x cm

Then, base of triangle is (x + 10) cm

Hence, altitude of triangle is 30 cm and base of triangle 40 cm

**Question 46:**

Let the altitude of triangle be x meter

Hence, base = 3x meter

Hence, altitude of triangle is 8 cm.

And base of triangle = 3x = (3 × 8) cm = 24 cm

**Question 47:**

Let the base of triangle be x meter

Then, altitude of triangle = (x + 7) meter

Thus, the base of the triangle = 15 m

And the altitude of triangle = (15 + 7) = 22 m

**Question 48:**

Let the other sides of triangle be x and (x -4) meters

By Pythagoras theorem, we have

Thus, height of triangle be = 16 cm

And the base of the triangle = (16 – 4) = 12 cm

**Question 49:**

Let the base of the triangle be x

Then, hypotenuse = (x + 2) cm

Thus, base of triangle = 15 cm

Then, hypotenuse of triangle = (15 +2 )= 17 cm

And altitude of triangle = = 8 cm

**Question 50:**

Let the shorter side of triangle be x meter

Then, its hypotenuse = (2x – 1)meter

And let the altitude = (x + 1) meter

**Question 51:**

Let x and y be the lengths of the two square fields.

∴ ——(1)

4x – 4y = 64

x – y = 16 ——(2)

From (2),

x = y + 16,

Putting value of x in (1)

Sides of two squares are 24m and 8m respectively.

**Question 52:**

Let the two numbers be x and y

Difference of the squares of the numbers

So the required numbers are 13 and 9.

**Question 53:**

Let the three consecutive numbers be x, x + 1, x + 2

Sum of square of first and product of the other two

Required numbers are 4, 5 and 6.

Hope given RS Aggarwal Solutions Class 10 Chapter 10 Quadratic Equations 10D are helpful to complete your math homework.

If you have any doubts, please comment below. A Plus Topper try to provide online math tutoring for you.

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