# GATE Questions

Q:

Every year before the festive season, a brand store increases the price of the product by 42% and then introduce two successive discount of 10% and 11% respectively. What is percentage loss and percentage gain ?

 A) 3.25% loss B) 13.742% loss C) 3.25% gain D) 13.742% gain

Explanation:

Let CP = 100,
42 % increase => SP = 142
10 % discount in SP => ((142 x 10)/100) = 14.2
So 1st SP = (142 - 14.2) = 127.8, again 12 % discount in 1st SP ((127.8 x 11)/100) = 14.058
2nd SP = (127.8 - 14.058) = 113.742,
So finally CP = 100, SP = 113.742, => gain = 13.742%.

3 2309
Q:

Artists are generally whimsical. Some of them are frustrated. Frustrated people are prone to be drug addicts.

Based on these statements which of the following conclusions is true?

 A) All frustrated people are drug addicts B) Frustrated people are whimsical C) All drug addicts are artists D) Some artists may be drug addicts

Explanation:

4 2289
Q:

A Certain sum of money an amounts to Rs 2500 in a span Of 5 years and further to Rs.3000 in a span of 7 years at simple interest The sum is ?

 A) Rs. 1800 B) Rs. 2000 C) Rs. 1400 D) Rs. 1250

Explanation:

2500 in 5th year and 3000 in 7th year
So in between 2 years Rs. 500 is increased => for a year 500/2 = 250
So, per year it is increasing Rs.250 then in 5 years => 250 x 5 = 1250
Hence, the initial amount must be 2500 - 1250 = Rs. 1250

7 2230
Q:

A vessel contains 20 liters of a mixture of milk and water in the ratio 3:2. 10 liters of the mixture are removed and replaced with an equal quantity of pure milk. If the process is repeated once more, find the ratio of milk and water in the final mixture obtained ?

 A) 5:3 B) 1:4 C) 4:1 D) 9:1

Explanation:

Milk = 3/5 x 20 = 12 liters, water = 8 liters

If 10 liters of mixture are removed, amount of milk removed = 6 liters and amount of water removed = 4 liters.

Remaining milk = 12 - 6 = 6 liters
Remaining water = 8 - 4 = 4 liters

10 liters of pure milk are added, therefore total milk = (6 + 10) = 16 liters.

The ratio of milk and water in the new mixture = 16:4 = 4:1

If the process is repeated one more time and 10 liters of the mixture are removed,
then amount of milk removed = 4/5 x 10 = 8 liters.

Amount of water removed = 2 liters.

Remaining milk = (16 - 8) = 8 liters.
Remaining water = (4 -2) = 2 liters.

Now 10 lts milk is added => total milk = 18 lts

The required ratio of milk and water in the final mixture obtained

= (8 + 10):2 = 18:2 = 9:1.

7 2228
Q:

A train running at the speed of 40 km/hr crosses a signal pole in 9 seconds. Find the length of the train ?

 A) 90 mts B) 150 mts C) 120 mts D) 100 mts

We know that   $\inline \fn_jvn \small speed = \frac{distance}{time}$
$\fn_jvn&space;\small&space;\Rightarrow$ distance= speed * time
$\fn_jvn&space;\small&space;\Rightarrow$ d = $\inline \fn_jvn \small 40\times \frac{5}{18}\frac{mts}{sec}\times 9$
$\fn_jvn&space;\small&space;\Rightarrow$  d= 100 mts.