SNAP 2006 Question Paper

The sequence is of prime numbers. 2003 is the next prime number

Let the number of student in Physics, Chemistry and Zoology be 4x, 3x and 5x respectively

New number of Physics student = 4x*(1+$$\frac{50}{100}$$) = 6x

New number of Chemistry student = 3x*(1+ $$\frac{25}{100}$$) = $$\frac{15x}{4}$$

New number of Zoology student = 5x * (1 + $$\frac{10}{100}$$) = $$\frac{11x}{2}$$

Required ratio is $$6$$ : $$\frac{15}{4}$$ : $$\frac{11}{2}$$

Multiplying overall by 4, answer is 24:15:22 

For every cycle of 2 days his overall earnings will be 5 Rs ,

In 8 cycles i.e in 16 days he will earn 40 Rs, on 17th day he will earn 20 more rupees and his overall savings will reach to 60 Rs. 

Let each alternate player plays for x minutes

Thus 4x = 90

x = 22.5 minutes

The profit fraction will be divided based on the amount spent and the investment time

For A, the investment = (20,000*5) +(15,000*7) = 205,000

For B, the investment = (20,000*5) + ( 16,000*7) = 212,000

For C, the investment = (20,000*5) + ( 26,000*7) = 282,000

Profit share of B = $$\frac{212000}{205000+212000+282000}$$ = $$\frac{212}{699}$$

Share of B = $$69900\times\ \frac{212}{699}$$ = 21200

For 1000 people, 32 person are born and 11 die.

Overall increase in population = 32-11 = 21

%increase in popoulation = $$\frac{21}{1000}\times\ 100$$% = 2.1%

Let the smaller number be denoted by $$x$$

The bigger number can be $$6x+15$$

Bigger number - smaller number = ($$6x+15$$) - ($$x$$)

$$5x+15$$ = 1365

$$5x$$ = 1350

$$x$$ = 270

Let AB and CD be the vertical poles such that the height of one is double to that of the other

It is given that the angles of elevation are complimentary. Thus let us assume the angle made by smaller tower be $$\theta\ $$. Then angle made by DE is $$90-\theta\ $$

In $$\bigtriangleup\ $$ ABC,  $$\tan\left(\theta\ \right) = \frac{\ h}{20}$$

In $$\bigtriangleup\ $$ CDE, $$\tan\left(\theta\ \right) = \frac{\ 20}{2h}$$

Equating the values of$$\tan\left(\theta\right)$$ we get, $$\ \frac{\ h}{20}=\ \frac{\ 20}{2h}$$ 

$$h^2\ =\ 200$$ $$\Rightarrow$$ $$h=14.14$$

Hence height of poles are $$14.14$$ and $$28.28$$

Using pythagoras theorem, we can clearly see from above that the shortest distance between Sameera and Meera is 10km.

Let number to be multiplied be $$x$$

Number obtained by the boy = $$35x$$

Actual answer = $$53x$$

Difference obtained = $$53x$$ - $$35x$$ = 1206

$$18x$$ = 1206

$$x$$ = 67