Quant Quiz – Mixed Problems – 6

Hello and welcome to exampundit. Here is a set of Quantitative Aptitude Quiz for upcoming Bank and Insurance Exams.

1. 20 college students are waiting in a queue for discount coupons of KFC. Each coupon costs ₹5. Ten of the students have the ₹5 coin and others have currency notes of ₹10. Determine in how many ways can all the 20 students stand in the queue such that the person at the coupon counter will not face any issue in paying back changes provided that the person at the counter does not have any changes.
a) 5513
b) 3434
c) 1200
d) 5678
e) Cannot be determined

Option: A

Explanation:

For the coupon seller to have change always, the person with ₹5 should come before the person with ₹ 10

We can also say that first person must have ₹5 and 20th person must have ₹10
→ let us take this case 5_ _ _(10 places), 10 _ _ _ (10 places),       no of cases  – 1

Take the first 10 numbers as one part and next 10 as second part
now take one 10 into the first part, this can be done in 9C1 ways because 1st number should be 5 always
and the 5 which is replaced by 10 can be arranged in 9C1 ways in 2nd part

one 10 is replaced, no of cases: 9C1x9C1 = 81
now replace two 10’s , 5  5 _ _ _ _ _ _ _ _ ; ……..10     —–   8C2 ways
5  10 5 _ _ _ _ _ _ _ ; …… 10     —–   7C1 ways
same will be the cases for two 5’s to be arranged in the second part
two 10’s are replaced, no of cases – (8C2 + 7C1)x(8C2 + 7C1) = 1225
replace three 10’s, 5 5 5 _ _ _ _ _ _ _; ……… 10       ——-  7C3 ways
5 10 5 5 _ _ _ _ _ _ ; ……… 10     ——– 6C2 ways
5 10 5 10 5 _ _ _ _ _ ; …….. 10     ——-  5C1 ways
three 10’s are replaced, no of cases – (7C3 + 6C2 + 5C1)x(7C3 + 6C2 + 5C1) = 3025
four 10’s replaced , no of cases : (6C4 + 5C3 + 4C2 + 3C1) 2  = 1156

five 10’s replaced , no of cases : (5C5 + 4C4 + 3C3 + 2C2 + 1C1) 2 = 25
max only five 10’s can come into first part
so total number of cases = 1+81+1225+3025+1156+25= 5513

2. Mousumi is a shopaholic. She went to a bag shop to buy a handmade wallet. She took ₹ 15 to the shop in the form of one rupee notes and 20 paise coins. After returning from the shop after buying the wallet, she was left with as many one rupee notes as she originally had 20 paise coins and as many 20 paise coins as she had originally one rupee notes. The total amount also reduced by two-third. What was the cost of the wallet?
a) ₹ 9.60
b) ₹11.50
c) ₹7
d) ₹5.75
e) None of the above

Option: A

Explanation:

Let number of one rupee notes=X

Number of 20 paise coins=Y

Mousumi started with (100X+20Y) and came back with (100Y and 20A) paise

Also, 100Y+20X=(1/3) (100X+20Y)

=>X=7Y

By hit and trial method,

Put Y=1=>X=7=>total ₹ 7.2 is less

Put Y=2=>X=14=>Total=₹ 14.4

This is correct.

Hence she spent=(2/3)x14.4=₹ 9.60=cost of wallet

3-4
In an island of the Maldives, the natives have a peculiar process of determining their average earnings and expenditures. According to an old tradition, the average monthly earnings had to be calculated on the basis of 14 months in the calendar year, while the average monthly expenditure was to be calculated on the basis of 9 months in the year. This weird system of calculation always resulted in the natives underestimating their savings because there occurs an underestimation of their earning. The expenditure per month gets overestimated. Now keeping the above points in view try to answer the below questions:

3. Mr. Ghosh comes to his native island from Africa and makes his native community comprising of 173 families to calculate their average earning and the average expenditure on the basis of 12 months per the calendar year. The average estimated earning in his community according to the old system is 77 fasios per month. Assuming there are no other changes, what will be the percentage change in savings of the 173 families?
a) 34% increase
b) 34 % decrease
c) No changes
d) 56 % increase
e) Cannot be determined

Option: E

Explanation:

Average Monthly earning (old system) = 77
So, Total Income of 173 families/14 = 77
So, Total Income of 173 families = 77×14
Now,

Average Monthly earning of 173 families (new system) =

Total Income/12 = 77×14/12 = 89.83 fasios
But, we do not know the average monthly expenditure in either system.
Nor do we know the savings.
So, the required answer cannot be determined.

4. In the previous question, the average estimated monthly expenditure is 21 fasios per month for the island. Determine the percentage change in the estimated savings of the 173 families.
a) 35 % decrease
b) 38 % increase
c) 32.3% increase
d) No changes
e) Cannot be determined

Option: C

Explanation:

Average Monthly Income (old system) = 77
So, Total Income of 173 families/14 = 77
So, Total Income of 173 families = 77×14
Now, Average Monthly Income of 173 families (new system) =

Total Income/12 = 77×14/12 = 89.83 fasios
Now, Average Monthly expenditure (old system) = 21
So Average Monthly Expenditure (new system) = 21×9/12 = 15.75

Total Savings (old system) = 77-21=56
Total Savings (new system) = 89.83-15.75 = 74.08
%change = (74.08-56)/56   x100 = 32.3%

5. Siddharth spends 30% of his income on his father’s medication, 20% on agricultural property and 10% on daughter’s education. The corresponding percentages for Akarsh are 40%. 25% and 13%. Given below are two conditions in 2 statements.
A.Siddharth spends more on agriculture than Akarsh.
B. Akarsh spends more on daughter’s education than Siddharth.
We can determine who spends more on Father’s medication with the help of which of the above statements?
a) Statement A alone but not by using statement B alone.
b) Statement B alone but not by using statement A alone.
c) Either of the statements alone.
d) both the statements together but not by either of the statements alone
e) cannot be answered on the basis of the two statements

Option: B

Explanation:

Let Siddharth’s and Akarsh’s total income be 100x and 100y respectively.

So the amount spent by Siddharth on father, agriculture and daughter will be 30x, 20x and 10x respectively.

The corresponding amounts spent by Akarsh will be 40y, 25y and 13y.
We need to find relation between 30x and 40y i.e. we need the ratio 3x/4y
Now let us consider statement A  alone:
We get 20x>25y
So 4x>5y i.e. x>1.25y
If  we take x=1.3y, then 3x/4y=3.9x/4y<1
But if x=2y, then 3x/4y=6y/4y>1
So statement A alone is not sufficient.

Consider statement B alone.
It says 13y>10x
So x<1.3y
For x=1.29y, 3x/4y = 3×1.29y/4y<1
Thus even for the highest value of x, we get 3x<4y.
For any value of x lesser than 1.29, 3x is surely going to be less than 4y.
So statement B is sufficient.

6. A pump can fill or empty an oil reservoir. The capacity of the oil reservoir is 3600m3. The filling capacity of the pump connected to the reservoir is 10m3/min less than its emptying capacity.If the pump takes 12 minutes extra to fill the reservoir than to empty it, determine the emptying capacity of the pump?
a) 50m³/min
b) 60m³/min
c) 45m³/min
d) 90m³/min
e) 80m³/min

Option: B

Explanation:

Let x m3/min be the filling capacity of the pump.

Therefore the emptying capacity=(x+10) m3/min

The time taken to fill the reservoir=3600/x

Time taken to empty the reservoir=3600(x+10)

It takes 12 more minutes to fill the reservoir than to empty it

{3600/x }   –    {3600/(x+10) }  =12

=>3600x+36000-3600x=12(x2+10x)

=>36000=12(x2+10x)

=>3000= x2+10x

=> x2+10x-3000=0

=>x=-60 or 50

Taking positive value of x=50

Emptying capacity =50+10=60 m3/min

7. Ronnie starts driving from the market to the Star’s lab in his car. Meanwhile, Dr. Stein also drives from the market one hour after Ronnie and overtakes Ronnie after covering 30% of the distance from market to the lab. Both of them continue the drive even after the overtaking. On reaching Star’s lab, Dr. Stein reverses his car and meets Ronnie’s car, after covering 23 1/3 of the distance between Star’s lab and the market. In how much time did Dr. Stein cover the distance between market to the lab? ( in hours)
a) 3
b) 5
c) 4
d) 3 1/3
e) 2 7/3

Option: D

Explanation:

Let the distance from market to Star’s lab be x

When Dr. Stein overtakes Ronnie for the first time, both of them cover= 3x/10

When Dr. Stein meets Ronnie after that, Dr. Stein covers (7x/10)+(7x/30) =28x/30

And Ronnie covers= (23x/30)-(9x/30)=14x/30

Therefore, Dr. Stein is twice as fast as Ronnie.

Dr.Stein starts one hour after Ronnie and catches up in 1 hour.

Thus, Dr. Stein covers 0.3x (30 % of x) in one hour or x in 10/3 hr or 3 1/3 h.

8. Anubhab spent less than ₹ 17500 to buy one quintal each of pomegranate, orange and guava. Which one of the following statements is sufficient ot determine which one of the three fruits bought was the costliest ?
A.2 kg pomegranate and 1 kg guava cost less than 1 kg pomegranate and 2 kg guava.
B.1 kg pomegranate and 2 kg orange together cost the same as 1 kg orange and 2 kg guava.
a) One of the statements alone but not the other statement alone
b) Either of the statements alone
c) Both statements together but not by using either statement alone
d) None of the above statements
e) Cannot be judged.

Option: C

Explanation:

From A alone, 2P+G<1+2G=>P<G

We got no idea about olive, so it is not sufficient.

From B alone, P+2P=O+2G => P+N=2G

This also is not alone.

Using both, As P<G and P+O=2G=> G<O

Hence both are required.

9. Nitu got an order for 480 khaddar blouses. She bought 12 charkhas and appointed some spinners to do it. However, many did not come on the working day. As a result, each of those who did come had to spin 32 more blouses than originally assigned with equal distribution of work. How many spinners had been appointed earlier and how many did not come?
a) 12,4
b) 10,3
c) 10,4
d) Cannot be determined
e) 11,7

Option: C

Explanation:

Solving by options,

Option a->

12 charkhas need to make 480 blouses.

Each charkha=40 blouses.

Due to the absence of few spinners, now each spinner had to make 40+32=72 blouses.

According to option, 12 are total spinners and 4 were absent hence 8 were spinning.

8 spinners made=8×72 >480 hence the option does not hold true.

Option c->

10 spinners did 480

One spinner did 48.

Remaining 6 spinners need to spin 48+32=130 blouse each

Tota 6 spinners will spin= 130x 6= 480 which satisfies the question

Hence answer is option C

10. A blind school has 3433 visually handicapped students. 80 to 85 percent of the students are good musicians and 30 to 40 percent of the students are good actors. Each student has excellence in at least one of the skills of music and acting. What is the absolute difference between the minimum and maximum possible numbers of students who are both great musicians and actors?
a) 338
b) 298
c) 208
d) 123
e) Cannot be determined

Option: B

Explanation:

Total Students = 2001
% of students who are musicians = 80% to 85% of 3433 = 2746 to 2918
So, % of students who are good in acting alone =

100%-85% to 100%-80% = 15% to 20% = 515 to 687
% of students who are good actors = 30% to 45% = 1030 to 1545
So, minimum = 1030-687=201
and maximum = 1545-515=499
and 499-201=298

Regards

Team EP

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