Quant Quiz – Mixed Problems – 5

1. Harshit decided to start a food chain outlet of his own eight years after his graduation. He invested Rs 30,00,000 in the food chain outlet business from which he expected a return of 6 % compounded annually. If the investment was planned to be double in 72/r years, where r is the interest rate p.a. , what can be the value of the total investment from this outlet business after 48 years?
A) 2,40,00,000
B) 3,60,00,000
C) 4,80,00,000
D) 67,00,000
E) None of these

Option: C

Explanations:

Let us consider P be the original amount.

Now we consider that it takes 12 years to become 2P at the rate of 6 % CI as 72/6=12.

P(1.06)^12=2P

=>P(1.06)^48=P{(1.06)^12}^4={(2)^4}P=16P

It shows that in 48 years the principal amount grows to become 16 times.

That is how in 12 years, 30 lakh becomes 480 lakh

2. Subham owns a juice outlet. He has hired a boy to take care of the business in the shop. The boy sells10 litres of juice from a juice bucket containing 40 litres of pure juice to Ram, the first customer. He then adds 10 litres of water to the bucket and again sells 10 litres of the mixture to Ramu, the 2nd customer and then again adds 10 litres of water to the bucket. Again he sells 10 litres of the mixture to Shyam, the 3rd customer who arrives at the shop and then adds 10 litres of water to the bucket and so on. Gopal arrives one person after the 3rd customer. Gopal’s juice will have how much amount of pure juice?
A) 510/128
B) 505/128
C) 410/128
D) 405/128
E) None of the above

Option: D

Explanations:

Initially total amount of pure juice = 40 L

Every time 10 L of juice ( or its mixture) is replaced with 10 L of water.

After every such operation, the quantity of juice in the total mixture becomes 3/4th.

As there are 4 such operations the net amount of juice in the mixture=40(3/4)^4=40(81/256)L

Since 5th customer( Gopal) purchases only 10 L amount of this mixture, therefore the amount of pure juice in his juice= 10(81/256)=405/128 L

3. 10 years ago the ages of Shyam and Priyanka were in the ratio 5:4. Presently, Shyam’s age is one-sixth more than Priyanka’s age. They married 10 years ago and now they have 6 children including a triplet and twins. The triplets, twins and the sixth child had their ages in the ratio 3:2:1. Recently one day Shyam had to attend a survey where he had to report the total age of the family. What can be the possible total age reported by Shyam?
A) 79
B) 93
C) 101
D) 107
E) None of these

Option: D

Explanations:

If today Priyanka’s age is 6y, then Shyam’s age is 6y+y=7y

10 years ago, Shyam’s age=5x and present age=7y

10 years ago, Priyanka’s age =4x and present age=6y

(5x+10)/(4x+10)=7y/6y

=> (5x+10)/(4x+10)=35x/30y         (y=5x)

=>(5x+10)/(4x+10)=7/6

Therefore, the current age of Shyam is 35 years and that of Priyanka is 30 years.

The age of triplets, twins and sixth child is 3k:2k:k

But it has been just ten years to their marriage, so the age of each triplet cannot exceed 10 years.

In that case, the maximum ages of each of the triplets, each of the twins and the sixth child are 9 yr, 6 yr and 3 yr respectively.

Therefore, the greatest possible value of present total age of the family = 35+30+3(9)+2(6)+3=107 years

4. Silumin and Magnox are the two alloys which were made by mixing Aluminium and Silicon in the ratio 6:9 and 7:11 respectively. If 40g silumin and 60 g alloy magnox are melted and mixed to form another alloy named Nambe, then what is the ratio of aluminium and silicon in Nambe?
A) 6:9
B) 59:91
C) 5:9
D) 59:90
E) None of these

Option: B

Explanations:

5. In a school, students were called for the flag hoisting ceremony on August 15. After the ceremony, small boxes of sweets were distributed among the students. In each class the student with roll no. 1 got one box of sweets, roll no. 2 got 2 boxes of sweet, and so on. In class 3 a total of 1200 boxes of sweets were distributed. By mistake one of the students of class 7th got double the sweets, he was entitled to get. Identify the roll number of the student who got twice as many boxes of sweets as compared to his entitlement?
A) 22
B) 28
C) 24
D) 30
E) None of these

Option: C

Explanations:

Let there be n students and the student with rol number k got double sweets where 0<k=<n, then we have

[n(n+1)]/2    +  K = 1200

=>n(n+1)=2400-2k

By hit and trial , we can easily figure out n<50 as n(n+1)<2400

Let us consider n=49 , then n(n+1)>2400

If we take n =48, n(n+1)=2352

=>n(n+1)=2400-48

=>n(n+1)=2400-2k

=>k=24

6. An oil reservoir in the shape of an inverted cone is connected with three pipes The cone has its base at the top. P and Q are two inlet pipes connected to the top of the reservoir which can fill the reservoir in 8 hours and 12 hours respectively. R is an outlet pipe which can empty the reservoir in 4 hours and is connected to the bottom. All the three pipes are opened when the reservoir is completely filled with oil. For continuous 20 hours, two out of three pipes are kept open and the third pipe remains open for a lesser time. This causes the height of the water inside the reservoir to come down to 50%. Which of the following conditions are possible for the above situation to take place?
A) P was open for 19 hours.
B) P was open for 19 hours 30 minutes.
C) Q was open for 19 hours 30 minutes.
D) R was open for 19 hours 50 minutes.
E) Not possible.

Option: C

Explanations: The LCM of 8, 12 and 4 =24
Now let’s assume the capacity of the reservoir=24L
=> The filling capacity of inlet P is 3 L/hr and that of Q is 2 L/hr.
Similarly, the capacity of outlet R is -6L/hr
When the height of the water comes down to 50%, then the water left in the cone is 1/8th of the total capacity i.e. 3L
By going through options:
A. 20(2-6)+19(3)=-23
Remaining water=24-23=1 which is not equal to 3 (hence wrong)
B. 20(2-6)+19.5(3)=-21.5
Remaining water=24-21.5=2.5 which is not equal to 3 ( hence wrong)
C. 20(3-6)+19.5(2)=-21
Remaining water=24-21=3 which is a possible case (hence correct)

7. Rakshit decided to invest a sum of money in mutual funds in the beginning of the year 2004. The accumulated interest was Rs.10,000 in the beginning of 2007 and in the beginning of 2010, the accumulated interest becomes Rs.25,000. The interest rate is compounded annually and the annual interest rate is fixed. The principal amount is:
A) 16000
B) 18000
C) 20000
D) 25000
E) None of these

Option: C

Explanations: Solving by options,
By taking option C,
Principal amount= Rs 20000
The in first 3 years it becomes Rs 30000 (=20000+10000), which is 1.5 times of Rs 20000.
Then in the next 3 years (same period), Rs 30000 should become Rs 45000, which is 1.5 times of Rs 30000.
As we can observe that in the first 3 years Rs 20000 yields Rs 10000 interest and in 6 years, Rs 20000 yields Rs 25000 interest at the same period of time, hence option C satisfies.

8. Dheeraj bought a solid metal cylinder of iron with dimensions 10 cm height and 14 cm diameter. But he did not find the cylindrical shape useful and hence melted it and re-cast it into two cones having their volumes in the ratio of 3: 4 without changing the height. Due to Dheeraj’s change in shape of the Iron, determine the percentage change in the flat surface area before and after?
A) 9%
B) 16%
C) 25%
D) 50%
E) None of these

Option: D

Explanations:

Volume of the cylinder= π x(7)^2 x 10 =490π

Vol of cone 1 + vol of cone 2= 490 π

=>210 π +280 π =490 π

Base area of cone 1 + base area of cone 2= 3(21) π +3(28) π =147 π

Flat surface area of cylinder= 2(π {7}^2) =98 π

% change in area= (147 π -98 π )/98 π      x100 = 50%

9. Arun is a wholesaler and he fixed the MRP of his typewriters at 55% above its production cost. The typewriter was then dispatched to a retailer named Harish to be sold in the local market, who plans to gain 23% profit on his purchase price. If Harish gives 10% discount on MRP, then find the profit percentage for Arun who sells his product to Harish calculated to the nearest integer?
A) 22%
B) 15%
C) 13%
D) 11%
E) None of these

Option: D

Explanations:

Arun sells the product to Harish, and then Harish sells to the buyer.

Assume production cost = 100 and Arun’s profit = x%

As MRP  of a product is 55% above its production cost,

MRP = 100(1 + 0.55) = 155

Harish gives 10% discount on MRP. So, buyer’s  price is 90% of MRP.

Arun makes x% profit, and Harish makes 23% profit.

So, 100(1 + x)×(1 + 0.23) = 155×0.9

x = 0.134

Hence, Arun’s profit = 13% (nearest integer)

10. Thiourea is a chemical produced by mixing Hydrogen and Sulphur in the ratio of 5: 4. Hydrogen is prepared by mixing two micro elements , P and Q, in the ratio of 1: 3. Sulphur is prepared by mixing two micro elements, Q and R, in the ratio of 2: 1. The final required industrial product is prepared by mixing 864 units of Thiourea with alcohol. If the concentration of the raw material P in the final mixture is 50%, how much alcohol had been added to Thiourea ?
A) 328 units
B) 368 units
C) 392 units
D) 616 units
E) None of the above

Option: B

Explanations:

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