[Download PDF] MAT 2013 Question Paper Paper with Solutions

Instructions

For the following questions answer them individually

Question 71

A manufacturer of a certain item can sell all he can produce at the selling price of ₹ 60 each. It cost him ₹ 40 in materials and labour to produce each item and he has overhead expenses of ₹ 3000 per week in order to operate that plant. The number of units he should produce and sell in order to make a profit of at least ₹ 1000 per week is

Video Solution

Solution

Let x be total items/week,

Selling Price (SP) will be 60x,

Cost Price (CP) will be [40x+4000 (extra 1000 for profit )]

So,

40x + 4000 = 60x

20x = 4000

x=200.

The number of units he should produce and sell in order to make a profit of at least ₹ 1000 per week is 200

Question 72

A jar full of whisky contains 40% alcohol. A part of this whisky is replaced by another containing 19% alcohol and now the percentage of alcohol was found to be 26%. What quantity of whisky is replaced ?

Video Solution

Solution

0% alcohol solution is mixed with 19% alcohol solution to give 26% alcohol solution.

w1/w2 = (A2 - Aavg)/(Aavg - A1)

= (40 - 26)/(26 - 19)

= 14/7 = 2/1

So 2 parts of 19% solution were mixed with 1 part of 40% solution. This means that 2/3rd of the 40% solution was replaced by 19% solution.

Question 73

A fair coin is tossed repeatedly. If head appears on the first four tosses, then the probability of appearance of tail on the fifth toss is

Video Solution

Solution

Probability of head=1/2

Because coin have only two chances tails or head.

And the statement that tails come 4 times will not affect the fifth toss.

So the probability of getting head=$$\frac{1}{2}$$

Question 74

The fuel indicator in a car shows $$\frac{1}{5}$$th of the fuel tank as full. When 22 more litres of fuel are poured into the tank, the indicator rests at three-fourth of the full mark. What is the capacity of the fuel tank?

Video Solution

Solution

Let the capacity of the fuel tank be x liters.

According to the question:

x/5 + 22 = 3/4x

On solving, we get

x = 40

So,

Capacity of the fuel tank = 40 litres.

Question 75

A sum of money is accumulating at compound interest at a certain rate of interest. If simple interest instead of compound were reckoned, the interest for the first two years would be diminished by ₹ 20 and that for the first three years, by 61. What is the sum?

Video Solution

Solution

P - sum and r- rate of interest

Simple Interest = Prt/100

Compound interest:

Amount = P(1+r/100)^n

P(r/100)^2= 40

P(r/100)^2 ×(300+r)/100 =61

On Solving, we get

P= 8000 (sum)

Question 76

A man covers a certain distance on a toy train. If the train moved 4 km/h faster, it would take 30 min less. If it moved 2 km/h slower, it would have taken 20 min more. What is the distance covered?

Video Solution

Solution

Let V be the peed and T be the time taken to cover the distance.

(V + 4)(T - 1/2) = (V - 2)(T+1/3).

(V + 4)(T - 1/2) = VT.

On solving, we get

V = 20 km/hr and T = 3 hours.

The distance = VT = 60 km.

Question 77

Two trains, 330 and 110 m long, are going in the same direction. The faster train takes one minute to pass the other completely. If they are moving in opposite directions, they pass each other completely in 3 s. What is the speed of the faster train?

Video Solution

Solution

Using the concept of relative velocity:

Total distance-240 m

When going in same direction

240/x-y=60

x-y=4

When going in different direction

240/x+y=3

x+y=80

On solving the equations we get,

x=42 and y=38

Speed of faster train is 42m/s

and slower one is 38m/s.

Question 78

The average age of all the students of a class is 18 yr. The average age of boys of the class is 20 yr and that of the girls is 15 yr. If the number of girls in the class is 20, then what is the number of boys in the class?

Video Solution

Solution

Let x = boys in class and y=girls in class = 20 (given).

Average = Sum of age/No. of students

Given Avg. of class is ={(20x+15(20))/(20+x)} = 18.

On solving, we get

x = 30

No.of boys in class is 30

Question 79

The total tractor population in a State is 294000, out of which 150000 are made by Mahindra & Mahindra. Out of every 1000 Mahindra tractors, 98 are red in colour. But only 5.3% of the total tractor population is red. Find the percentage of non-Mahindra tractors that are red.

Video Solution

Solution

Mahindra red tractor=98/100*(150000)=147000

Total red tractor=294000*.53=155820

Non Mahindra red tractor=155820-147000

= 8820

i.e 8820/294000

=.03

=3%

Question 80

If 7% of the total quantity of wheat is lost in grinding when a country has to import 12 million tonne but when only $$5 \frac{1}{5}$$ % is lost it can import 3 million tonne, then what is the quantity of wheat grown in the country?

Video Solution

Solution

Difference in % of whet lost = 7 - 26/5 = 9/5%

Difference in import = 12 - 3 = 9 million

As 9/5% of total qty of wheat = 9 million

So, 9x/500=9

Therefore, x = 500 million.

CAT Content

MAT 2013 Question Paper

A jar full of whisky contains 40% alcohol. A part of this whisky is replaced by another containing 19% alcohol and now the percentage of alcohol was found to be 26%. What quantity of whisky is replaced ?

A fair coin is tossed repeatedly. If head appears on the first four tosses, then the probability of appearance of tail on the fifth toss is

The fuel indicator in a car shows $$\frac{1}{5}$$th of the fuel tank as full. When 22 more litres of fuel are poured into the tank, the indicator rests at three-fourth of the full mark. What is the capacity of the fuel tank?

A sum of money is accumulating at compound interest at a certain rate of interest. If simple interest instead of compound were reckoned, the interest for the first two years would be diminished by ₹ 20 and that for the first three years, by 61. What is the sum?

A man covers a certain distance on a toy train. If the train moved 4 km/h faster, it would take 30 min less. If it moved 2 km/h slower, it would have taken 20 min more. What is the distance covered?

Two trains, 330 and 110 m long, are going in the same direction. The faster train takes one minute to pass the other completely. If they are moving in opposite directions, they pass each other completely in 3 s. What is the speed of the faster train?

The average age of all the students of a class is 18 yr. The average age of boys of the class is 20 yr and that of the girls is 15 yr. If the number of girls in the class is 20, then what is the number of boys in the class?

The total tractor population in a State is 294000, out of which 150000 are made by Mahindra & Mahindra. Out of every 1000 Mahindra tractors, 98 are red in colour. But only 5.3% of the total tractor population is red. Find the percentage of non-Mahindra tractors that are red.

If 7% of the total quantity of wheat is lost in grinding when a country has to import 12 million tonne but when only $$5 \frac{1}{5}$$ % is lost it can import 3 million tonne, then what is the quantity of wheat grown in the country?

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