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QUESTION: 1

Solution:
Let the son's present age be x years

Then, man's present age = (x + 24) years

∴ (x + 24) + 2 = 2(x + 2)

⇒ x + 26 = 2x + 4

⇒ x = 22

Then, man's present age = (x + 24) years

∴ (x + 24) + 2 = 2(x + 2)

⇒ x + 26 = 2x + 4

⇒ x = 22

QUESTION: 2

The roots of 2x²-6x+3=0 are

Solution:

QUESTION: 3

Solution:

QUESTION: 4

Three math classes : X, Y and Z take an algebra test

1. The average score of class X is 83

2. The average score of class Y is 76.

3. The average score of class Z is 85.

4. Average score of class X and Y is 79.

5. Average score of class Y and Z is 81.

What is the average score of classes X, Y, Z?

Solution:

Let the number of students in class x, y & z be a, b and c respectively

Then,

Total of x = 83 a

Total of y = 76 b

Total of z = 85 c

And,

QUESTION: 5

For Rs 300 you can buy either packet-1 containing 9 paper weight and 7 ball pens or pacjet-II containing 6 paper weight and 13 ball pens. The price of each paper weight is

Solution:
Let Price of each paper weight be Rs. x and ball Pens be Rs. y

9x + 7y = 300 .....(i)

6x + 13y = 300 .....(ii)

Solving (i) & (ii) we get

y = 12 & x = 24

9x + 7y = 300 .....(i)

6x + 13y = 300 .....(ii)

Solving (i) & (ii) we get

y = 12 & x = 24

QUESTION: 6

A classroom has equal number of boys and girls.8 girls left to play Kho-Kho,leaving twice as many boys as girls in the classroom. What was the total number of girls and boys present initially?

Solution:
Let number of boy and girls in class are x & y

Then, x = 2 (y - 8)

or x = 2y - 16

again, x = y

or 2y - 16 = y

or y = 16

Total Number of boys & girls are 32

Then, x = 2 (y - 8)

or x = 2y - 16

again, x = y

or 2y - 16 = y

or y = 16

Total Number of boys & girls are 32

QUESTION: 7

Area of a square field is 1 hectare. The length of another square field is 1% more than the length of this square field. The difference in their areas is

Solution:

1 hectare = 10000 m^{2}

Area of a square field = 10000 m^{2}

let length of a square field be x m

then x^{2} = 10000

x = 100m

length of other square field = 100 + 100 x 1/100 = 101

Area of Another square field = (101)^{2} = 10201 m^{2}

∴ Difference in their areas = 10201 - 10000

= 201 m^{2}

QUESTION: 8

A circular running path is 726 metres in circumference. Two men start from the same point and walk in opposite directions at the speed of 3.75 km. per hour and 4.5 km per hour respectively. Then when will they meet for first chance:

Solution:

The two men walk in opposite directions @ 62.5 metres/minute and 75 metres/minute respectively

∴ They will meet for the first time after

QUESTION: 9

In Arun's opinion, his weight is greater than 65 kg but less than 72 kg. His brother does not agree with Arun and he thinks that Arun's weight is greater than 60 kg but less than 70 kg. His mother's view is that his weight cannot be greater than 68 kg. If all of them are correct in their estimation, what is the average of different probable weights of Arun?

Solution:

QUESTION: 10

What is the perimeter of the rectangle ABCD when AD = 3, and BD = 5

Solution:

QUESTION: 11

The foot of th eperpendicular from the point (2, 4) upon x + y = 1 is

Solution:

QUESTION: 12

A sum of money invested at Compound Interest amounts to Rs 640 at the end of first year and Rs 676 at the end of second year. The sum of money is closest to

Solution:

QUESTION: 13

What is the smallest number that has to be added to 710 so that the sum is a perfect cube?

Solution:

QUESTION: 14

A shopkeeper marks his sarees at 20% above the cost price and allows the purchaser a discount of 10% for cash buying. What profit per cent does he make?

Solution:

QUESTION: 15

Which is the largest among the following fractions? 5/8, 2/3, 7/9, 3/5, 4/7

Solution:

QUESTION: 16

A polygon has 5 diagonals. The polygon is

Solution:

QUESTION: 17

AB and CD are two straight lines. Transversal EF intersects them as shown in the given figure. If b = c then

Solution:

Clearly x + y = 180°

QUESTION: 18

PT is a tangent and PAB is a secant to the circle. If PT = 5 cm and PA = 4 cm then the length of AB is

Solution:

QUESTION: 19

The sides of a triangle ABC are 21 metres, 20 metres and 13 metres respectively. The longest side is AB. If a perpendicular CD is drawn from C on AB, then the difference of the area (in sq. metres) of the 2 triangles ACD and BCD will be

Solution:

QUESTION: 20

If two numbers are in the ratio of 2:3 and the product of their HCF and LCM is 33750,then the sum of the numbers is

Solution:

QUESTION: 21

Two villages are 2 km apart.If the angles of depression of these villages when observed from a plane are found to be 45°and 60° respectively,then the height of the plane is

Solution:

QUESTION: 22

An integer is 10 more than its one-third. The integer is

Solution:

QUESTION: 23

If x% of y is equal to z, what percent of z is x?

Solution:

QUESTION: 24

A boy,after giving away 80% of his pocket money to one companion and 6% of the remainder to another, has 47 paise left with him. How much pocket money did the boy have in the begining ?

Solution:

QUESTION: 25

Taps A and B can fill a bucket in 12 minutes and 15 minutes respectively. If both are opened and A is closed after 3 minutes, how much further time would it take for B to fill the bucket?

Solution:

QUESTION: 26

What per cent of selling price would be 34% of cost price if gross profit is 26% of the selling price?

Solution:

QUESTION: 27

A merchant bought 60 sheeps at Rs 120 per sheep. He sold 40 of them at Rs 150 each. 10 of them died. What should be the selling price of the remaining sheeps if he wants a profit of Rs 800?

Solution:

QUESTION: 28

If Rs. 1066 are divided among A, B, C and D such that A : B = 3 : 4, B : C = 5 : 6 and C : D = 7 : 5, who will get the maximum

Solution:

QUESTION: 29

In a ΔABC, A=90º . Then is equal to

Solution:

QUESTION: 30

A and B have monthly incomes in the ratio 5:6 and monthly expenditures in the ratio 3:4. If they save Rs 1800 and Rs 1600 respectively,find the monthly income of B.

Solution:

QUESTION: 31

In a G.P. if the (m + n)th term is p and the (m - n) th term is q, then its mth term is

Solution:

QUESTION: 32

Rs 5000 earned Rs 300 interest in 2 yrs. The rate of interest is

Solution:

QUESTION: 33

(169-144)¹∕² ÷ (64+36)¹∕²=?

Solution:

QUESTION: 34

A man reduces his speed a two-third to walk a distance and consequently becomes late by one hour. With his usual speed, he covers the same distance in

Solution:

QUESTION: 35

P can complete a work in 12 days working 8 hours a day. Q can complete the same work in 8 days working 10 hours a day. If both P and Q work together, working 8 hours a day, in how many days can they complete the work?

Solution:

QUESTION: 36

The angle subtended at the centre of a circle of radius 3 m by the arc measuring 1 m is:

Solution:

QUESTION: 37

The value of cos²θ+sec²θ is always

Solution:

QUESTION: 38

If cos (A - B)=3/5 tan A tan B=2, then

Solution:

QUESTION: 39

Into a circular drum of radius 4.2 m and height 3.5 m how many full bags of wheat can be emptied if space required for each wheat bags is 2.1m^{3}.

Solution:

QUESTION: 40

A hall is 15 m long and 12 m broad. If the sum of the areas of the floor and the ceiling is equal to the sum of areas of the four walls, the volume of the hall is :

Solution:

QUESTION: 41

A cylinder with base radius of 8 cm and height of 2 cm is melted to form a cone of height 6 cm. The radius of the cone will be :

Solution:

QUESTION: 42

**Above graph shows the percentage growth in population in six states A, B, C, D, E, and F from 1994 to 1995 and 1995 to 1996. Study the graph and answer their questions.**

**Q. **Population of State 'F' in 1995 was approximately what percent of its population in 1996 ?

Solution:

= 66.66%

≈67%

[Let population in 1995 be 100 then population in 1996 is 150]

QUESTION: 43

**Above graph shows the percentage growth in population in six states A, B, C, D, E, and F from 1994 to 1995 and 1995 to 1996. Study the graph and answer their questions.**

**Q. **If the population of State 'B' in the year 1994 was 5 lakh, what was approximately its population in the year 1996?

Solution:

Population of B in 1996 = 5 × 1.55 × 1.35 lakh = 10.4625 lakhs

≈10.5 lakhs

QUESTION: 44

**Above graph shows the percentage growth in population in six states A, B, C, D, E, and F from 1994 to 1995 and 1995 to 1996. Study the graph and answer their questions.**

**Q. **If the population of States C and D in 1995 are in the ratio 2 : 3 respectively and the population of State 'C' in 1994 was 2.5 lakhs, what was the population of State D in 1995 ?

Solution:

Popualtion of C : Population of D = 2 : 3

Hence Population of D in 1994

= 3.75 × = 6 lakh

Population of D in 1995 = 3.75 lakhs

QUESTION: 45

**Q. **In 1994 the population of States B and D are equal and the population of State B in 1996 is 20.925 lakhs. What approx. was the population of State 'D' in 1996 ?

Solution:

Let population of B in 1994 be x

Then x × 1.55 × 1.35 = 20.925 lakhs

⇒ x = 10 lakhs

As in 1994, population of D = Population of B Hence Population of D in 1994 is 10 lakhs Population of D in 1996 is = 10 × 1.6 × 1.7 lakh = 27.2 lakh

≈27 lakhs

QUESTION: 46

**The pie chart given below shows the funding arrangements for National Highways Development Projects-Phase 1. Study the chart carefully to answer these questions.
Funding arrangements for NHDP-I(total cost: Rs.30,000 Crores) **

**Q. **Near about 25% of the funding arrangement is through

Solution:

QUESTION: 47

**The pie chart given below shows the funding arrangements for National Highways Development Projects-Phase 1. Study the chart carefully to answer these questions.
Funding arrangements for NHDP-I(total cost: Rs.30,000 Crores) **

**Q. **The angle of the segment formed at the center of the pie chart, representing Cess/Market borrowings is approximately

Solution:

QUESTION: 48

**The pie chart given below shows the funding arrangements for National Highways Development Projects-Phase 1. Study the chart carefully to answer these questions.
Funding arrangements for NHDP-I(total cost: Rs.30,000 Crores) **

**Q. **If the toll is to be collected through an outsourced agency by allowing a maximum of 10% commission. How much amount should be permitted to be collected by the outsourced agency, so that the project is supported with Rs.1,690 Crores?

Solution:

Amount required to be permitted = 1690/0.9 = Rs 1878 crore

QUESTION: 49

**The pie charts show estimated revenue and expenditure budgets for 2004-2005 for country X.
Notes: 1. Corporate tax revenues increased by Rs.2545 crore in the budget estimates for 2004-2005 over the estimates for 2003-2004.
2. Service tax brings in Rs.3990crore according to the budget for 2004-2005.
3. Total expenditure on defence increased by a whopping 28 percent from Rs.6030crore in 2003-2004 to Rs.7700crore in 2004-2005.**

**Q. **The revenue generated by Custom duty, Income tax and Corporate tax according to the budget for 2004-2005 is.

Solution:

QUESTION: 50

Notes: 1. Corporate tax revenues increased by Rs.2545 crore in the budget estimates for 2004-2005 over the estimates for 2003-2004.

2. Service tax brings in Rs.3990crore according to the budget for 2004-2005.

3. Total expenditure on defence increased by a whopping 28 percent from Rs.6030crore in 2003-2004 to Rs.7700crore in 2004-2005.

**Q. **What is the percentage increase in the revenue generated by corporate tax is 2004-2005 over 2003-2004 according to the budgets?

Solution:

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