LIC AAO | IBPS/SBI SO | QUANT QUIZ - 8 | S W A G

Directions (Q. 1-10): Study the following information carefully and answer the given questions.

1)If the price of petrol increases by 25% and Raj intends to spend only an additional 15% on petrol, by how much % will he reduce the quantity of petrol purchased?
a)10%
b)12%
c)8%
d)6.67%
e)12.5%

EXPLANATION :-
Let the price of 1 litre of petrol be Rs.x and let Raj initially buy 'y' litres of petrol.
Therefore, he would have spent Rs. xy on petrol.

When the price of petrol increases by 25%, the new price per litre of petrol is 1.25x.

Raj intends to increase the amount he spends on petrol by 15%.
i.e., he is willing to spend xy + 15% of xy = 1.15xy

Let the new quantity of petrol that he can get be 'q'.
Then, 1.25x * q = 1.15xy
Or q = (1.15/1.25)y = 0.92y.

As the new quantity that he can buy is 0.92y, he gets 0.08y lesser than what he used to get earlier.
Or a reduction of 8%.

OR

100*100 = 10000
125*X = 11500
X = 92
SO REDUCED QUANTITY = 8%


2)If a merchant offers a discount of 40% on the marked price of his goods and thus ends up selling at cost price, what was the % mark up?

a)28.57%
b)40%
c)66.66%
d)58.33%

EXPLANATION :- 

If the merchant offers a discount of 40% on the marked price, then the goods are sold at 60% of the marked price.

The question further states that when the discount offered is 40%, the merchant sells at cost price.

Therefore, selling @ 40% discount = 60% of marked price (M) = cost price (C)

i.e.,60/100 M = C

 a mark up 66.66%

Correct answer choice (3)

3)Ram completes 60% of a task in 15 days and then takes the help of Rahim and Rachel. Rahim is 50% as efficient as Ram is and Rachel is 50% as efficient as Rahim is. In how many more days will they complete the work?

a)13 (1/3)
b)8(1/3)
c)5(5/7)
d)7(5/7)

EXPLANATION :-

Ram completes 60% of the task in 15 days.
i.e., he completes 4% of the task in a day.

Rahim is 50% as efficient as Ram is.
Therefore, Rahim will complete 2% of the task in a day.

Rachel is 50% as efficient as Rahim is
Therefore, Rachel will complete 1% of the task in a day.

Together, Ram, Rahim and Rachel will complete 4 + 2 + 1 = 7% of the work in a day.
They have another 40% of the task to be completed.
Therefore, they will take 40/7 more days to complete the task.

4) Ram covers a part of the journey at 20 kmph and the balance at 70 kmph taking total of 8 hours to cover the distance of 400 km. How many hours has been driving at 20 kmph?

a)2 hours
b)3 hours 20 minutes
c)4 hours 40 minutes
d)3 hours 12 minutes

EXPLANATION :-

Let x be the number of hours he travels at 20 kmph.
Distance covered in this x hours = 20x km
He would have therefore, traveled the balance (8 - x) hours at 70 kmph.

Distance covered in this (8 - x) hours = (8 - x) * 70 = (560 - 70x) km
The total distance traveled = 20x + 560 - 70x = 400
=>160 = 50 x
=>x = (160/50) hours = 3.2 hours = 3 hours and 12 minutes

               OR

400/8 =50
20_____________________70
__________50_____________
20:30
2:3
so 2*8/5 =16/5 = 3.2 hours = 3 hours 12 minutes


5)A sample of x litres from a container having a 60 litre mixture of milk and water containing milk and water in the ratio of 2 : 3 is replaced with pure milk so that the container will have milk and water in equal proportions. What is the value of x?

a)6 litres
b)10 litres
c)30 litres
d)None of these

EXPLANATION :-

The best way to solve this problem is to go from the answer choices.

The mixture of 60 litres has in it 24 litres of milk and 36 litres of water. (2 : 3 :: milk : water)
When you remove x litres from it, you will remove 0.4 x litres of milk and 0.6 x litres of water from it.

Take choice (2). According to this choice, x = 10.

So, when one removes, 10 litres of the mixture, one is removing 4 litres of milk and 6 litres of water.   

Therefore, there will be 20 litres of milk and 30 litres of water in the container.   

Now, when you add 10 litres of milk, you will have 30 litres of milk and 30 litres of water – i.e. milk and water are in equal proportion.

         OR



36__________________0
_________30____________
30 : 6
5 : 1
1/6 *60 = 10



6)Shyam can do a job in 20 days, Ram in 30 days and Singhal in 60 days. If Shyam is helped by Ram and Singhal every 3rd day, how long will it take for them to complete the job?

a)12
b)16
c)15
d)10

EXPLANATION :-

As Shyam is helped by Ram and Singhal every third day, Shyam works for 3 days while Ram and Singhal work for 1 day in every 3 days.

Therefore, the amount of work done in 3 days by Shyam, Ram and Singhal = 3/20 + 1/30 +1/60 = 1/5 th of the job. Hence, it will take them 5 times the amount of time = 3*5 = 15 days.

7)One year payment to the servant is Rs. 200 plus one shirt. The servant leaves after 9 months and recieves Rs. 120 and a shirt. What is the price of the shirt?

a)Rs.80
b)Rs.100
c)Rs.120
d)Cannot be determined

EXPLANATION :-

The servant worked for 9 months instead of 12 months, he should receive 9/12 of his annual payment

Let the price of 1 shirt be Rs.S.

i.e., 3/4 (200 + S).

However, the question states that the servant receive Rs. 120 + S where S is the price of the shirt.

By equating the two equations we get  3/4 (200 + S) = 120 + S.

Therefore Price of the shirt S = Rs. 120.

Correct answer choice (3)

8)The monthly incomes of A and B are in the ratio 4 : 5, their expenses are in the ratio 5 : 6. If 'A' saves Rs.25 per month and 'B' saves Rs.50 per month, what are their respective incomes?

a)Rs.400 and Rs.500        
b)Rs.240 and Rs.300
c)Rs.320 and Rs.400
d)Rs.440 and Rs.550

EXPLANATION :-

Let A's income be = 4x
A's expenses, therefore = 4x - 25

Let B's income be = 5x
B's expenses, therefore = 5x - 50

We know that the ratio of their expenses = 5 : 6
=>24x - 150 = 25x - 250
=>Therefore, x = 100.
=>A's income = 4x = 400 and B's income = 5x = 500.

9)If the perimeter of a rectangle is 138 metres and the difference between the length and the breadth is 7 metres, what is the area of the rectangle? 

a) 1216 square metres
b) 1147 square metres
c) 1184 square metres
d) 1178 square metres
e) None of these

EXPLANATION :-

Let the length and breadth of the rectangle be x and y respectively.
Then the perimeter of rectangle = 2(x + y)
Now,2(x + y) = 138
 x + y = 69 ...(I)
Difference of length and breadth = x – y = 7 ...(II)
Solving (I) and (II), we get x = 38 metres
y = 31 metres.
Area of rectangle = x × y = 38 × 31
= 1178m2


10)A fort has provisions for 60 days. If after 15 days 500 men strengthen them and the food lasts 40 days longer, how many men are there in the fort?

a)3500
b)4000
c)6000
d)None of these

EXPLANATION :-

Let there be 'x' men in the beginning so that after 15 days the food for them is left for 45 days.

After adding 500 men the food lasts for only 40 days.

Now (x+500) men can have the same food for 40 days.

Therefore by equating the amount of food we get,

45 * x = (x + 500) * 40

45x = (x+500) * 40

5x = 20,000

x = 4,000

Therefore there are 4,000 men in the fort.

THANK YOU :)