353 – [173 – {x – (125 – 237)}] = 427

⇒ 353 – [173 – {x – (– 112)}] = 427

⇒ 353 – [173 – {x + 112}] = 427

⇒ 353 – [173 – x – 112] = 427

⇒ 353 – [61 – x] = 427

⇒ 353 – 10 + x = 427

⇒ x = 427 – 343 = 84

Sum of the interior angles of a convex polygon with n sides = (n – 2) × 180°

Sum of the exterior angles of a convex polygon = 360°    ... (1)

Let each exterior angle be A°. Then each interior angle will be 90 + A°

The sum of an exterior and its corresponding interior angle is 180°

∴ A + (90° + A) = 180°

⇒ A = 45°

Sum of the exterior angles of a convex polygon = 360°   … (from 1)

i.e., if the polygon has 'n' sides, then n × A = 360

∴ Number of sides of the regular polygon, n = 360/measure of one exterior angle = 360/45 = 8 sides.

Let age of son 2 years ago be = x

Age of man 2 years ago would be = 6x

As per question after 10 years;

2 × age of son = age of man

⇒ 2(x + 2 + 10) = (6x + 2 + 10)

⇒ 2x + 24 = 6x + 12

⇒ 4x = 12

⇒ x = 3 years

∴ Present age of son = 3 + 2 = 5 years

Present age of man = 6x + 2 = 6 × 3 + 2 = 20 years

The share of A : B is 3 : 4

The share of B : C is 2 : 3

⇒ A : B : C = 3 × 2 : 4 × 2 : 4 × 3

⇒ A : B : C = 6 : 8 : 12

⇒ A : B : C = 3 : 4 : 6

Sum of ratios = 13

Now, the share of B = [4/13] × 8645 = 2660

Share of C = [6/13] × 8645 = 3990

∴ The difference between the share of B and C = 3990 – 2660 = 1330

C’s work for 1 day = 1/12

A and B complete 1/2 and C completed 1/12 × 2 = 1/6

Completed work before D joined is 1/2 + 1/6 = 4/6

The work completed by D = 1 – 4/6 = 2/6 of work

Now project uncompleted after D left = 1/12

⇒ D did = 2/6 – 1/12 = 3/12 of work

He worked for 4 days, means he complete 3/12 of work in 4 days

⇒ He can do complete project in 12/3 × 4 = 16 days

Slope of line (m) = (3 – 7)/(– 2 – 5) = – 4/–7 = 4/7

Equation of line:  y – y₁ = m(x – x₁)

⇒ y – 7 = 4/7(x – 5)

⇒ 7(y – 7) = 4(x – 5)

⇒ 7y – 49 = 4x – 20

⇒ 4x – 7y + 29 = 0

Let the number of members be x.

x member contribute is Rs. x and each member also contributes x paisa.

So total Rupees is

x² + x²/100 = 4949

101x² = 4949×100

x² = 49 × 100

x= 70

Let the number = x

Divisor = 273+327= 600

Quotient = 3×(327-273) = 46×3= 138

Remainder = 16

X= divisor × quotient + remainder

X= 600 × 138 + 16

X= 82816

According to the question,

3A = 7B

A/B = 7/3 and 5B = 3C, B/C = 3/5

Ratio of efficiency of A, B and C is 7 : 3 : 5

A can do total work in 14 days,

So total work = 14 × 7 = 98

A, B and C take time = 98/(7+3+5) = 98/15 = 6 8/15 days

According to the question,

(x – 2)(x + 3)/{(x + 3)(x – 1) = 6/7

(x-2)/(x-1) = 6/7

7x – 14 = 6x – 6

X = 8