Arithmetic (UPSC) Part- III

⇒ 8x - 12000 = 9x - 18000
∴ x = ₹ 6,000
Total income of x and y = (3 + 4)x
= ₹ 6,000 × 7 = ₹ 42,000

⇒ 81 = 64 + 1 + (d)² ⇒ (d)² = 16 ⇒ d = 4

3 Adults = 5 children ∴ 1 adult = 5/3 children

12 Adults + x children = 18 Adults

12 × 5/3 children + x children = 18 × 5/3 children

x = 10 children

He paid 8650 then amount left
= 25650 - 8650 = 17000
Amount to be paid after 2 years
= 17000 + 17000 × 12.5/100 = 17000 + 2125 = 19125

He paid 9125 at the end of 2nd year then remaining amount
= 19125 - 9125 = 10000
Amount to be paid at the end of 3rd year
= 10000 + 10000 × 12.5/100 = 11250

Checking statement 1
x − y = 8
Both x and $y$ must be positive for any value of $x$ and$y$.
It is not true because negative values of $x$ and $y$ or positive $x$ and negative $y$ is also possible.

Checking statement 2
If x is positive, y must be negative for any value of x and $y$.
It is also not true because positive values of x and $y$ are also possible.

Checking statement 3
If $x$ is negative, y must be positive for any value of $x$ and $y$.
Here if $x$ is negative then only negative value of $y$ is possible.
Hence, neither 1 nor 2 nor 3

Each equilateral triangle is made by joining the three points as in the figure given below. Circle is divided into three sectors.

Hence, required number of triangles = 24 / 3 = 8

∴ 60 × 100/40 = 150