[Download PDF] MAT 2008 Question Paper Paper with Solutions

Instructions

For the following questions answer them individually

Question 51

If the price of gold increases by 30%, find by how much the quantity of ornaments must be reduced so that the expenditure may remain the same as before.

Video Solution

Solution

The price of gold increases by 30%

let the initial price be x

let the initial consumption by y

since the price of gold increases by 30 %

final price of gold =1.3x

now, expenditure=price*consumption

let the final consumption be z

given total expenditure remains constant

Therefore

x*y=1.3 x *z

Therefore z=(y/1.3)

% decrease=((initial consumption-final consumption)/initial consumption)*100%

Therefore,

% decrease=((y-z)/y)*100%=(1-(1/1.3))*100%=(1-0.769)*100%=

= 23 1/13%

Question 52

A monthly return railway ticket costs 25 per cent more than a single ticket. A week’s extension can be had for the former by paying 5 per cent of the monthly ticket’s cost. If the money paid for the monthly ticket (with extension) is Rs 84, the price of the single ticket is

Video Solution

Solution

Let x be the price of single ticket

Return railway ticket = 125x/100

5% of return ticket = 5/100 * 125x/100 = 25x/400 = x/16

Given : 125x/100 + x/16 = 84

Solving for x, we get

x=64

Question 53

A papaya tree was planted 2 years ago. It increases at the rate of 20% every year. If at present, the height of the tree is 540 cm, what was its height when the tree was planted?

Video Solution

Solution

Let the height at time of plantation be h.

now, height = 540 = 6/5*6/5*h

36/25h = 540

h = 540*25/36 = 375 cm

Question 54

A mixture of 40 litres of milk and water contains 10% water. How much water should be added to this so that water may be 20% in the new mixture?

Video Solution

Solution

In mixture: 40 l

Milk = 36 l

Water = 4 l

Let x amount of water be added, so

4 + x = 20/100 (40 + x)

Solving for x, we get

x = 5 litres

Question 55

The amount of water (in ml) that should be added to reduce 9 ml lotion, containing 50% alcohol, to a lotion containing 30% alcohol, is

Video Solution

Solution

Lotion = 9 ml

Alcohol = 4.5 ml

water = 4.5 ml

Let water be added is x ml

so, x + 4.5 = 70% of (9 + x) [since alcohol is 30%, so water is (100-30) = 70%]

x = 6 ml

Question 56

The average of marks obtained by 120 candidates was 35. If the average of the passed candidates was 39 and that of the failed candidates was 15, then the number of those candidates who passed the examination, was

Video Solution

Solution

T = total students, P =passed, F = failed students

AVERAGE = SUM OF MARKS OF ALL STUDENTS/ NUMBER OF STUDENTS

A = 35 = ΣT/120

ΣT = ΣF + ΣP = 120*35 = 4200 ---(1)

and ΣP = 39*P, ΣF = 15*F [F = 120-P]

Putting values of ΣP and ΣF in equation 1, we get

4200 = 15(120-P) + 39P

4200 = 1800 - 15P + 39P

24P = 2400

P = 100 (passed students)

Question 57

Angad was conducting an experiment in which the average of 11 observations came to be 90, while the average of first five observations was 87, and that of the last five was 84. What is the measure of the 6th observation?

Video Solution

Solution

Let the sum of first 5 numbers be x and last five be yand 6th observation be t.

So, by averages formula, we get

x + t+ y = 11*90 = 990 ...-(1)

x = 87*5 = 435

y = 84*5 = 420

So, putting values in equation 1, we get

435 + t + 420 = 990

t = 135

Question 58

The average age of an adult class is 40 years. 12 new students with an average age of 32 years join the class, thereby decreasing the average by 4 years. The original strength of the class was

Video Solution

Solution

Le the number of students originally in a class be n.

By averages concept,

ΣN = 40n

Σnew = 32*12 = 384

new average = 36

ΣN + Σnew = 36(n+12)

40n + 384 = 36n + 432

4n = 48

n = 12

Question 59

The average age of 8 persons in a committee is increased by 2 years when two men aged 35 years and 45 years are substituted by two women. The average age of these two women is

Video Solution

Solution

Let the average age of members of committee be A and 2 women be a and b.

ΣM = A * 8

ΣM +a + b - 35 - 45 = 8*(A + 2)

8A + a + b - 35 - 45 = 8*(A + 2)

a+b = 96

Average age of 2 women = 96/2 = 48 years

Question 60

At Narmada Sarovar bachao (NSB) demonstration, supporters of Ms Patkar outnumbered the police by 9 : 1. The police arrested 135 NSB supporters averaging 5 for every 3 policemen. How many supporters of NSB were there in the demonstration?

Video Solution

Solution

The number of police involved in the security operation

= $3/ 5 \times 135$

= 81

Thus, the required number of supporters = $81 \times 9$

= 729

CAT Content

MAT 2008 Question Paper

If the price of gold increases by 30%, find by how much the quantity of ornaments must be reduced so that the expenditure may remain the same as before.

A monthly return railway ticket costs 25 per cent more than a single ticket. A week’s extension can be had for the former by paying 5 per cent of the monthly ticket’s cost. If the money paid for the monthly ticket (with extension) is Rs 84, the price of the single ticket is

A papaya tree was planted 2 years ago. It increases at the rate of 20% every year. If at present, the height of the tree is 540 cm, what was its height when the tree was planted?

A mixture of 40 litres of milk and water contains 10% water. How much water should be added to this so that water may be 20% in the new mixture?

The amount of water (in ml) that should be added to reduce 9 ml lotion, containing 50% alcohol, to a lotion containing 30% alcohol, is

The average of marks obtained by 120 candidates was 35. If the average of the passed candidates was 39 and that of the failed candidates was 15, then the number of those candidates who passed the examination, was

Angad was conducting an experiment in which the average of 11 observations came to be 90, while the average of first five observations was 87, and that of the last five was 84. What is the measure of the 6th observation?

The average age of an adult class is 40 years. 12 new students with an average age of 32 years join the class, thereby decreasing the average by 4 years. The original strength of the class was

The average age of 8 persons in a committee is increased by 2 years when two men aged 35 years and 45 years are substituted by two women. The average age of these two women is

At Narmada Sarovar bachao (NSB) demonstration, supporters of Ms Patkar outnumbered the police by 9 : 1. The police arrested 135 NSB supporters averaging 5 for every 3 policemen. How many supporters of NSB were there in the demonstration?

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