Question

A car is moving with a speed of 100 km/h. If the speed of car first increases by x% and then decreases by x%, the final speed of the car is 96 km/h. The value of x is ______.

विकल्प

• 4

• 20

• 8

• 10

Answer 1

A car is moving with a speed of 100 km/h. If the speed of car first increases by x% and then decreases by x%, the final speed of the car is 96 km/h. The value of x is 20.

Explanation:

Original speed of car = 100 km/h

Speed of car after increase

= 100 + x% of 100

= `100 + x/100 xx 100`

= (100 + x) km/h

Now the final speed of car after decrease of x%

= `(100 + x) - x/100 xx (100 + x)`

= `(100 + x)[1 - x/100]` km/h

Also, given final speed of car = 96 km/h

∴ `(100 + x)(1 - x/100) = 96`

∴ (100 + x)(100 – x) = 9600

`\implies` (100)² – x² = 9600   ...[∵ (a + b)(a – b) = a² – b²]

`\implies` 10000 – x² = 9600 

`\implies` x² = 10000 – 9600 = 400

`\implies` x = ± 20

`\implies` x = 20  ...[∵ x > 0]