Explanation: Let x and y be the respective km's travelled by man via taxi and by his own car.

Given x + y = 135 => x = 135 - y

But according to the question,

7x + 6y = 900

7(135-y) + 6y = 900

=> 945 - 7y + 6y = 900

=> y = 945 - 900= 45

=> x = 135 - 45 = 90

Therefore, the distance traveled by taxi is 90 km.

Explanation:

The diameter of circle will be = √ (12² + 16²) = 20 m

So, the radius of circle will be = 20/2= 10 m

Therefore, area = π × 102 = 100π

Explanation: Let, length is 7x m and breadth is 3x m.

ATQ,

2(7x + 3x) = 200

⇒ 10x = 100

⇒ x = 10

So, the length is 7 × 10 = 70

Explanation:

Let, the natural number be x

and reciprocal number 1/x

ATQ, x + 12 = 160 * 1/x

⇒ x² + 12x – 160 = 0

⇒ x² + (20x − 8x) −160 =0

⇒ x² + 20x − 8x – 160 = 0

⇒ x (x + 20) −8(x + 20) =0

⇒ (x + 20) (x− 8) = 0

⇒ x = 8

[x≠−20 because it is not a natural number]

Hence, the required natural number is 8

Explanation: His regular wage is 250 tk.

So, he needs to earn = 1000 - 250 = 750 from commission

Let, he needs to sell TK. X to required amount of commission.

ATQ, 15% of X = 750

Or, X = 5000

Explanation:

2¹²+2¹²+2¹²+2¹²

= 4.2¹²

= 2².2¹²

= 2²⁺¹²

= 2¹⁴

Explanation:

Father get the cake of 1/4 part

Remaining = 1 - 1/4 part = 3/4 part

Let, the number of family is x

Another member will get = 1/ (3 × 4) = 1/12 part

Now, x/12 = 3/4

x = 9

Total member = 9 + 1 = 10

Explanation:

2x + 3y = 100 .... (1)

3x + 2y = 120 .... (2)

Multiply by 3 in Equation (1) and multiply by 2 in Equation (2) and then subtract

6x + 9y = 300

6x + 4y = 240

Or, 5y = 60

Or, y = 12

Therefore, x = 32

Explanation:

Let, The cost price of X = 100x

So, the cost price of Y = 128x

and the cost price of Z = 128x - 128x × (25/100) = 96x

ATQ, 100x - 96x = 2

or, x = 0.5

Therefore, the cost price of X = 100x = 100 × 0.5 = 50

Explanation: Given distance=360 km.

Let the speed of the train be x km/hr.

Speed when increased by 5 km/hr =(x+5) km/hr

ATQ,

360​/x − 360/(x+5) ​= 1

Or, x² + 5x − 1800 = 0

Or, x² + 45x − 40x − 1800 = 0

Or, x (x + 45) − 40(x + 45) = 0

Or, (x − 40) (x + 45) = 0

Or, x = 40, −45

The speed of the train is 40 km/hr.

Explanation:

Now, ∆ABC = 3∆ADE

Or, ADE/ABC = 1/3 = AE²/AC²

Or, AE: AC = 1: √3

Explanation: Students taking physics = 30 (these 30 include those 13 that take both)

Students taking English = 25 (these 25 also include those 13)

So those that take either physics or English or both = 30 + 25 - 13 = 42.

Required percentage = 42/90 × 100 = 47% approx.

Explanation: The answer is = (5 - 3) × 2 = 4

Explanation: For the first three-month interest of Tk 10000 = 10p

For each month after three-month interest of Tk 10000 = 10 × 9q

Total interest = 10(p + 9q)

Explanation:

Let the number of buffaloes be x and the number of ducks be y.

Each buffalo has 1 head & 4 legs.

Each duck has 1 head & 2 legs.

So, the number of heads = x + y and the number of legs = 4x + 2y.

So, by the given condition,

4x + 2y = 2(x + y) + 24

⇒ 4x − 2x + 2y − 2y = 24

⇒ 2x = 24

⇒ x = 12

Explanation:

2015: (5000 × 2) + 5000 = 15000tk.

2020: (15000 × 2) + 5000 = 35000tk

2025: 35000 × 2 = 70000tk

Explanation: 0.0675 can write = 67.5 × 10-3

= 6.75 × 10-2

= 0.675 × 10-1

But, 0.00675 × 10² = 0.675.  which is not equal 0.0675

Thus, the answer is 0.0675

Explanation: Temperature on the fourth day = [(40.2 × 4 + 41.3 × 4) - (40.6 × 7)] ° C = 41.8° C

Explanation:

3x + 2y = 8 ... ... ...(i)

2x - 2y = 2 ... ... ...(ii)

Adding equation (i) and (ii) we have

5x = 10

Or, x = 2

Therefore, 4 – 3 × 2 = -2

Explanation: Let, B's present age is x year & 10 years ago he was (x - 10)

After 10 years, A = 2((x - 10), B = (x + 10)

Now, 2(x + 10) - (x + 10) = 9

Or, x = 39