# Simplification Problems for SSC CGL

1.

The population of a city A which is 68000 decreases at the rate of 1200/year. Population of city B which is 42000, increases at the rate of 800 per year. Find in how many years, the population of cities A and B are equal?

A.) 9 years
B.) 13 years
C.) 15 years
D.) 10 years

We have to find the population of cities A and B after x years.
Step 1: Population of city A = 68000, decreases at the rate of 1200/year
68000 – 1200x
Step 2: Population of city B = 42000, increases at the rate of 800/year
42000 + 800x
Step 3: Find after how many population of cities A and B are equal.
Population of city A = Population of city B
68000 – 1200x = 42000 + 800x
68000 – 42000 = 1200x + 800x
26000 = 2000x
x = 13

2.

6156  ÷ √? × 53 = 4028

A.) 6889
B.) 6561
C.) 6995
D.) 6235

6153 × 53/√? = 4028
⇒ √? = 80.96 ≈ 81
⇒ ? = 6561

3.

Simplify: 13.05 × 4.5 ÷ 0.5

A.) 119.75
B.) 117.45
C.) 115.50
D.) 140.60

No bar, No bracket. Hence, first step starts from ‘DMAS’
Step 1: Divide 4.5 ÷ 0.5=9
Step 2: Multiply 13.05 × 9 = 117.45

4.

98643 – 21748 = 51212 + ?

A.) 25683
B.) 26687
C.) 27893
D.) 26874

Given eqn,
98643 – 21748 = 51212 + ?
⇒ ? = 98643 – 21748 – 51212
⇒ ? = 25683

5.

If x/y = 3/4 and 8x + 5y = 22, then find the value of x.

A.) 1.5
B.) 2.3
C.) 4.5
D.) 3.6

y = 4/3 x
Substitute this value in 8x+5y=22
8x + 5(4/3) x = 22
44x=66
x=1.5