IIFT 2020 QA questions and solutions

Previous year paper questions for IIFT 2020 QA

1. IIFT 2020 QA | Arithmetic - Percentage

Maruti-Suzuki Company manufactures the Ciaz cars at its Manesar facility. The company employs labour and capital/machine as inputs in a 2 : 1 ratio of their quantities. The cost of one unit of labour (think it as wage per hour) is 500 rupees and the cost of one unit of capital (machine running cost per hour) is 1500 rupees. The total labour and capital cost for the monthly production is 5 crore rupees.
Due to economic slowdown, the company has decided to reduce monthly production to half.
Meanwhile, the labour cost has decreased by 20% and the capital cost has gone up by 20%. Find the total capital and labour cost the company would now incur for the monthly production.

A.
2.4 crores
B.
2.6 crores
C.
2.8 crores
D.
3 crores

Answer: Option B

Explanation :

Let the labour employed by the company be 2x and the capital be x.
Thus, the total cost of running production for an hour = 500 × 2x + 1500 × x = 2500x
Total cost for running the production for a month = 5 Crores = 5 × 10⁷
Total number of hours the production is done = x = $\frac{5 \times 10^{7}}{2500}$ = 20000
Since the production is cut in half, the total hours = 0.5 × = 20000 = 10000
Labour costs decreased by 20% and the capital cost increased by 20%.
Thus, the total cost per hour = 500 × 2x × 0.8 + 1500 × x × 1.2 = 2600x
Since x = 10000, the total cost = 2600 × 100000 = 2.6 Crores.
Hence, the answer is option B.

2. IIFT 2020 QA | Modern Math - Permutation & Combination

Refer to the figure given below. AB, CD and EF are three parallel paths. A person starts from AB to reach EF by moving in four steps - moving from AB to O₁ in step 1, from O₁ to CD in step 2, from CD to O₂ in step 3 and from O₂ to EF in step 4. If he takes a curved path in one step, he cannot take a curved path in the next step. In how many ways the person can reach EF from AB?

A.
128
B.
256
C.
32
D.
64

3. IIFT 2020 QA | Algebra - Simple Equations

The product of the roots of the equation $\sqrt[3]{11 + 2 x}$ + $\sqrt[3]{11 - 2 x}$ = 2 is approximately equal to:

A.
22
B.
-27
C.
35
D.
-33

Answer: Option D

Explanation :

Cubing the given equation, we have:

(a + b)³ = a³ + b³ + 3 ∙ a ∙ b(a + b)

11 + 2x + 11 - 2x + 3 ∙ ${(11 + 2 x)}^{\frac{1}{3}}$ ${(11 - 2 x)}^{\frac{1}{3}}$ (a + b)

Given a + b = 2.

Hence:

22 + 3 ∙ ${(11 + 2 x)}^{\frac{1}{3}}$ ${(11 - 2 x)}^{\frac{1}{3}}$ (2)

= 22 + 6 × $({(121 - 4 x^{2})}^{\frac{1}{3}})$ = 8

Cubing this we get: 121 - 4x² = $- \frac{343}{27}$

4x² = 121 + $\frac{343}{27}$ = $\frac{3610}{27}$

x² = 33.42

One root would be + $\sqrt{33.42}$ and the other - $\sqrt{33.42}$ .

The product of the roots would be approximately -33.

4. IIFT 2020 QA | Arithmetic - Average

Sumit stays in Noida in a joint family comprising of his parents, uncle, aunt, an elder sister and a cousin two years younger than him. Sumit completed his MBA in 2013, from a reputed B-School.
That year, the average age of Sumit's family was 41. Sumit got married in 2015 and two years after he became father. If the average age of Sumit's family in 2019 remains same as in 2013, and Sumit is older than his wife by 3 years, at what age did Sumit graduate MBA?

A.
31
B.
35
C.
38
D.
41

5. IIFT 2020 QA | Arithmetic - Profit & Loss

A fruit seller in a locality uses dishonest practice as follows:
(i) He cheats on weight by 10 percent for every 1kg weight.
(ii) He pushes up the price of fruit by 15 percent and then gives a discount of 8 percent to the buyers for every kg sold.
Find the percentage profit of the fruit seller from sale of 1kg. (Profit is defined as Revenue - Cost)

A.
18.95
B.
17.56
C.
16.04
D.
15.00

Answer: Option B

Explanation :

Let the cost of fruit be Rs. 100 for 1000gm.
The fruit seller marks the price by 15% and then gives a discount of 8%. Thus, the selling price of fruit = Rs. 105.8
The fruit seller also cheats the customers by 10% of the weight. Thus, he sells 900gm for Rs. 105.8
Cost Price = $\frac{100}{1}$ = Rs. 100/kg

Selling price = $\frac{105.8}{0.9}$ = Rs. 117.56

Percentage profit = $\frac{117.56 - 100}{100}$ × 100 = 17.56%

Hence, the answer is option B.

6. IIFT 2020 QA | Algebra - Simple Equations

If 16x = $\frac{64}{256^{y}}$ and 9x = $\frac{9}{3^{y}}$ , then the values of x and y are respectively,

A.
$\frac{5}{6}$ and $\frac{1}{2}$
B.
$\frac{7}{6}$ and $\frac{1}{3}$
C.
$\frac{5}{6}$ and $\frac{1}{3}$
D.
$\frac{11}{6}$ and $\frac{1}{3}$

7. IIFT 2020 QA | Arithmetic - Simple & Compound Interest

Mr. Madhukar worked for 5 years in a multi-commodity trading company after graduating from a reputed B-School. He then resigned from his job and started an online garment export business. For his business Madhukar used Rs. 8,00,000/- of his own savings and borrowed Rs. 12,00,000/- from a private sector bank in April, the beginning month of the financial year. Mean while, RBI eased repo rate in May and banks passed on the benefits to the borrowers. As a result, Madhukar borrowed an additional Rs. 9,00,000/- after 4 months at an interest rate which is 10% lower than the interest rate of his earlier borrowing. If the total interest paid by Madhukarat the end of that year on both the loans is Rs. 1,39,200/-, what is the interest rate per annum on first borrowing?

A.
6%
B.
7%
C.
8%
D.
9%

8. IIFT 2020 QA | Geometry - Circles

In the figure, a circle of radius 2 cm is inscribed in a square. There are four smaller circles at each of the cornerof the square. Whatis the total area covered by all the five circles?

A.
4π + 4π(6 - 4 $\sqrt{2}$ )² cm²
B.
4π + 4π(3 - 2 $\sqrt{2}$ )² cm²
C.
4π + 4π(12 - 8 $\sqrt{2}$ )² cm²
D.
4π + 4π(9 - 6 $\sqrt{2}$ )² cm²

9. IIFT 2020 QA | Arithmetic - Time & Work

Surojit Ghosh left his IT job last year and started a food business with his wife Debjani. They named the business "Bong's Kitchen". Surojit takes hours more when he works alone compared to when
he works jointly with his wife. On the other hand, Debjani takes 28 $\frac{1}{2}$ hours more than what she takes
when she works with Surojit. How long approximately will it take, Surojit to complete the business
work alone ?

A.
6 hours
B.
9 hours
C.
12 hours
D.
15 hours

Answer: Option D

Explanation :

Let the number of hours needed by Surojit working alone be S hours and the number of hours required by Debjani when she works alone be D.
The time required to finish the work when they work together = $\frac{S ∙ D}{S + D}$
Hence, we can frame the given 2 conditions as:

S - $\frac{S ∙ D}{S + D}$ = $\frac{21}{5}$ ...(1)

D - $\frac{S ∙ D}{S + D}$ = $\frac{141}{5}$ ..(2)

Solving the two equations simultaneously, we get S = 15 hours approx

10. IIFT 2020 QA | Arithmetic - Time, Speed & Distance

Three friends Pradeep, Suresh and Subodh workin the same office. During an extended weekend they decided to go together on a family trip to Corbett National Park. They started from office in their own car but at different time and travelled in the same direction at speeds of 50 km/hr, 60 km/hr and 75 km/hr respectively. Suresh and Subodh overtook Pradeep at the same point. If Suresh started 90 minutes after Pradeep, how many minutes after Pradeep did Subodh start from the office?

A.
120
B.
150
C.
180
D.
210

11. IIFT 2020 QA | Geometry - Quadrilaterals & Polygons

ABCD is a parallelogram whose diagonals are parallel to the lines 2y - x - 5 = 0 and y + 2x - 7 = 0 respectively.

Then ABCD is -

A.
Cyclic quadrilateral
B.
Rectangle
C.
Cube
D.
Rhombus

12. IIFT 2020 QA | Arithmetic - Simple & Compound Interest

Suhani, an enterprising lady took the loan from M/s Koramattam Finance against her gold ornaments at a simple interest of 12% per annum for 2 years. She, then, loaned 50% of the amount received from M/s Koramattam Finance, to Vishamber at the rate of 16% per annum compounded half yearly for 2 years and the remaining amount to Kalawati at the rate of 12% per annum compounded annually for 2 years. What was the approximate percentage earning of Suhani at the end of 2 years?

A.
42%
B.
28%
C.
50%
D.
60%

13. IIFT 2020 QA | Modern Math - Probability

A Financial Analyst estimates that the probability that the economy will experience recession in next one year is 30%. He also believes that in case of recession, the probability that his mutual funds will increase in value is 20%. He also believes that if there is no recession the probability that the value of mutual funds will increase in value is 75%. Find the probability that mutualfunds value will increase.

A.
0.285
B.
0.525
C.
0.585
D.
0.60

14. IIFT 2020 QA | Algebra - Simple Equations

The probabilities of three mutually exclusive outcomes of an experiment 0.25(1 - x), 0.5(1 - 2x) and 0.25(1 + 4x) respectively.

Which of the following holds for the value of x ?

A.
-0.5 ≤ x ≤ 0.5
B.
0 ≤ x ≤ 0.5
C.
-0.75 ≤ x ≤ 0.25
D.
-0.25 ≤ x ≤ 0.5

15. IIFT 2020 QA | Arithmetic - Time, Speed & Distance

Two cities Mathura and Agra, 48 kms apart, are located on the bank of River Yamuna. A motor boat goes from Mathura to Agra and returns back as soon as possible. Yamuna flows at a speed of 6 km/hr.
The motorboat completes the trip from Mathura to Agra and back in not more than 6 hours.

Assuming the motorboat does nothalt at Agra, what should be the minimum speed of motorboatin still water?

A.
16 km/hr
B.
18 km/hr
C.
25 km/hr
D.
27 km/hr

Answer: Option B

Explanation :

Let the river flow from Mathura to Agra. Let the speed of boat in still water be S kmph
Hence, if journey is to be done in 6 hours, then:

$\frac{48}{S + 6}$ + $\frac{48}{S - 6}$ = 6

Solving this equation, we get: (S - 18)(S + 2) = 0 which gives us S = 18 kmph

16. IIFT 2020 QA | Geometry - Basics

A man, from the foot of the building P, walks towards the building Q. After walking for 2 mts, he finds that buildings P and Q makean angle of elevation of 60° and 30° respectively. If building Q is 1.5 mts high, find the distance between the tops of both buildings P and Q.

A.
5 mts
B.
4 mts
C.
$(\sqrt[2]{3} - 1.5)$ mts
D.
$(1 - 1.5 \sqrt{3})$ mts

17. IIFT 2020 QA | LR - Clocks

At what time between 10.00 AM and 11.00 AM,the minute hand and the hour hand of a watch would make an angle of 180°?

A.
10.20 AM
B.
10.22 AM
C.
10.23 AM
D.
10.25 AM

18. IIFT 2020 QA | Arithmetic - Profit & Loss

An owner of a grocery shop purchases two varieties of grain. The price of first variety is twice the price of the second one. He mixes both the varieties and sells the mixture at the price of Rs. 28 per kg, making a profit of 25%. If the ratio of first variety of grain and the second variety of grain in the mixture is 2 : 3, find the price of first variety of grain.

A.
Rs. 16/kg
B.
Rs. 24/kg
C.
Rs. 32/kg
D.
Rs. 64/kg

19. IIFT 2020 QA | Arithmetic - Time, Speed & Distance

As shown in the diagram, Ram started from point A along the chord AB and Shyam started from D along the chord DC. AB and DC are two equal chords. Ram and Shyam move with the same speed and started at the same time. After some time, Ram reached "M" which is the midpoint of AB.
Ram and Shyam now make an angle at the centre O. If the distance between Ram and Shyam is 6 m now,then how much distance each will walk before they meet each other?

A.
6√3
B.
3√3
C.
2√3
D.
5√3

20. IIFT 2020 QA | Geometry - Triangles

A circle is inscribed in a right angled isosceles triangle. O is the centre of the circle which touches the triangle ABC at X, Y, Z. If AB = 7√2 cm, then the ratio of AZ : BX : CY -

A.
1 : (√2 - 1) : 1
B.
1 : 1 : (√2 - 1)
C.
1 : 1 : ( $\sqrt{2}$ - $\frac{1}{2}$ )
D.
1 : ( $\sqrt{2}$ - $\frac{1}{2}$ ) : 1

Answer: Option B

Explanation :

If ACB is a right angled isosceles triangle and AB is hypotenuse with length 7*( $\sqrt{2}$ ) length, then sides AC and BC = 7 cm
Now, the circle inscribed is an incircle.
Radius of in-circle = {7 + 7 - [7*( $\sqrt{2}$ )]}/2 = 7 - $\frac{7 \sqrt{2}}{2}$
Now, if center of circle is marked as O, then quadrilateral OZCY is a square.
Hence, CY = CZ = 7 - $\frac{7 \sqrt{2}}{2}$
Hence, AZ = 7 - 7 - $\frac{7 \sqrt{2}}{2}$ = $\frac{7 \sqrt{2}}{2}$
Also, BX = BY and BY = BC - CY = $\frac{7 \sqrt{2}}{2}$
Hence, BX = $\frac{7 \sqrt{2}}{2}$

Hence, the given ratio becomes 1 : 1 : [( $\sqrt{2}$ ) - 1]

21. IIFT 2020 QA | Arithmetic - Profit & Loss

Saudi Aramco and Reliance Industries entered into a joint venture where Saudi Aramco invested 20 billion dollars and Reliance Industries invested 30 billion dollars. The ownership ratio is always equal to the investment ratio. After 1 year, the venture made a profit of 6 billion dollars which they reinvested. Now Reliance Industries wants to increase its ownership to 75%, how much it should pay to Saudi Aramco in billion dollars?

A.
12.4
B.
8.4
C.
10.4
D.
14.4

22. IIFT 2020 QA | Algebra - Simple Equations

Consider the equation (x - a)(x - b) = 0 which has two identical roots. What should be the condition under which (x - a) (x - b) = c has two distinct real roots?

A.
c > 0
B.
a + b > 0
C.
c(a + b) > 0
D.
ab > 0

Answer: Option A

Explanation :

(x - a)(x - b) = 0 having identical roots means a = b
Hence, the expression now effectively becomes (x - a)(x - a) = c
For x to have different values, we should have c > 0 because at c = 0, we will end up with x = a AND c < 0 is not possible for rational values of a and x.
For c > 0, we will have x = a + ( $\sqrt{c}$ ) and x = a - ( $\sqrt{c}$ )

23. IIFT 2020 QA | Arithmetic - Time & Work

A water tanker can be filled by 2 pipes A & B separately in 16 min & 32 min respectively. Outlet of the tanker is partially open and it can empty the full tanker completely in 1 hour 4 min. Pipes A & B were opened simultaneously for 9 min to fill the tanker but the partially open outlet was not closed. After 9 min the pipes A & B were closed and the tanker then went to Mohan's house, 6 km away to deliver water. If the tanker moved at a constant speed of 36 km/hr, approximately what percentage of tanker was full, when it reached Mohan's house?

A.
55%
B.
63%
C.
58%
D.
None of the options

24. IIFT 2020 QA | Arithmetic - Average

An economic survey of total 1000 participants was carried out in Delhi, Mumbai, Kolkata and Chennai about their wealth. 300 participants reported possessing both a house and a car. 500 participants reported possessing both a house and a motorbike. 200 participants reported possessing a house together with a motorbike and a car. Find the number of participants who possess both a house and car, or possess both a house and a motorbike.

A.
400
B.
200
C.
600
D.
800

25. IIFT 2020 QA | Geometry - Basics

ABC is an isosceles triangle. BDE, EFG, GHI and IJC are four equal isosceles triangles inside ABC triangle. D and F,F and H,H and J are connected by circular arcs. The angle ABC is 30 degrees and BE is 1m. What is the area of the shaded region?

A.
$\sqrt{6}$ - $\frac{π}{6}$ m²
B.
$\sqrt{5}$ - $\frac{π}{5}$ m²
C.
$\sqrt{3}$ - $\frac{π}{3}$ m²
D.
$\sqrt{7}$ - $\frac{π}{7}$ m²

Answer: Option C

Explanation :

Since ∠ABC = 30° and ∆DBE is an isosceles triangle, ∠BDE = 120°

Applying the cosine rule in △BDE.

BE² = BD² + DE² - 2 × BD × DE cos(120)

1 = 2BD² + BD² [since BD = DE]

BD = $\frac{1}{\sqrt{3}}$

Thus, BD = DE = EF = FG = GH = HI = IJ = JC = $\frac{1}{\sqrt{3}}$

Area of △BDE = $\frac{1}{2}$ × BD × DE × sin(120) = $\frac{1}{2}$ × $\frac{1}{\sqrt{3}}$ × $\frac{1}{\sqrt{3}}$ × $\frac{\sqrt{3}}{2}$ = 4 $\frac{1}{\sqrt{3}}$

The total area of all smaller isosceles triangles = 4 × 4 $\frac{1}{\sqrt{3}}$ = $\frac{1}{\sqrt{3}}$ m²

∠DEF = ∠FGH = ∠HIJ = 120°
Thus, the total area of circular arcs = π × ( $\frac{1}{\sqrt{3}}$ )² = $\frac{π}{3}$ m²

Now, side BC = BE + EG + GI + IC = 4m

Using the cosine rule in △ABC, we get AB = AC = $\frac{4}{\sqrt{3}}$ .

Thus, Area of △ABC = $\frac{1}{2}$ × $\frac{4}{\sqrt{3}}$ × $\frac{4}{\sqrt{3}}$ × sin(120) = $\frac{4}{\sqrt{3}}$ m²

Thus, the area of the shaded region = Area of △ABC - Area of smaller isosceles triangles - Area of the circular sections

= $\frac{4}{\sqrt{3}}$ - $\frac{1}{\sqrt{3}}$ - $\frac{π}{3}$ = $\sqrt{3}$ - $\frac{π}{3}$

Hence, the answer is option C.

IIFT 2020 QA | Previous Year IIFT Paper

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