## Ques 1.

X, Y and Z are situated at the bank of river which is flowing at a constant rate. Y is at an equal distance with X and Z. A swimmer Aviral takes 10 h to swim from X to Y and Y to X. Also, he takes 4 h to swim from X to Z. What is the ratio of speed of Aviral in still water and speed of stream?

**Solution :**

Speed with stream " u " =a+b

Speed against stream "v"=a-b

Distance between X to Z = 2D

Speed against stream "v"=a-b

Distance between X to Z = 2D

==>2D/u = 4 hours

==> D=2u

==> D=2u

D/u + D/v = 10 hours

==>2u/u + 2u/v = 10

==>u/v=4

put u nd v value.

==>a+b/a-b = 4

==>a/b = 5/3

==>2u/u + 2u/v = 10

==>u/v=4

put u nd v value.

==>a+b/a-b = 4

==>a/b = 5/3

## Ques 2.

If s1 nd s2 be the surface area of a sphere and the curved surface area of the circumscribed cylinder respectively, then s1 is equal to?

**Solution :**

Radius of cylinder= r

Height=2r

S1= 4πr²

S2=2πr×2r=4πr²

Height=2r

S1= 4πr²

S2=2πr×2r=4πr²

S1=S2

## Ques 3.

8,12,24,60,180,630 ?

**Solution :**

12= 8*1.5

24= 12*2

60= 24*2.5

180= 60*3

630= 180*3.5

630*4 = 2520

24= 12*2

60= 24*2.5

180= 60*3

630= 180*3.5

630*4 = 2520

## Ques 4.

A train starts from Jammu for Srinagar at 13:30 and reaches at 17:30. Another train starts from Srinagar at 15:30 and reaches Jammu at 19:00. At what time both train meet?

**Solution :**

Speed of first train D/4

Speed of second train D/7/2=2D/7

Second train starts 2 hrs after first train so,distance travelled by first train by that time is (D/4)*2=D/2

Speed of second train D/7/2=2D/7

Second train starts 2 hrs after first train so,distance travelled by first train by that time is (D/4)*2=D/2

So,for remaining distance time taken by both trains is equal to meet each other so, (2D/7)*T=D/2-(D/4)*T

T=14/15=56 mins

13:30+56mins=16:26

## Ques 5.

A and B can do a piece of work in 30 days .A having worked for 16 days , B finished the remaining work alone in 44 days .In how many days shall B finish the whole work alone?

**Solution :**

A and B did work in 30 days ==> 30A+30B=1 --- i

A works for 16 days and B works for 44 day ==>16B+44B=1 --- ii

solving A,B from i and ii

We get 1/60

so B done 1/60 days

## Ques 6.

A contractor employed 25 labourers on a job. He was paid 275 for the work. After retaining 20% of this sum, he distributed the remaining amount amongst the labourers. If the number of men to women labourers was in the ratio 2 : 3 and their wages in the ratio 5 : 4, what wages did a woman labourer get ?

**Solution :**

Men 25×2/5= 10

Women 25×3/5=15

Wage each man 5x

Woman 4x

Women 25×3/5=15

Wage each man 5x

Woman 4x

20% of amount retaining = 275* 20% = 55

Remaining amount = 275-55=220

==>10×5x + 15×4x= 220

==>110x= 220

==>x= 2

Wages of women = 4X = 4×2=8

==>110x= 220

==>x= 2

Wages of women = 4X = 4×2=8

## Ques 7.

A certain amount was to be distributed among A,B,C in the ratio 3:4:5 respectively,but was erroneously distributed in the ratio 9:4:7 respectivly. As a result of this B got 260 less. What is the amount?

**Solution :**

3+4+5 = 12

9+4+7 = 20

( 3:4:5 ) *20 = 60:80:100 = 240 parts

( 9:4:7 ) *12 = 108:48:84

Error in B = 80-48 = 32 parts

B less than 260 with error.

32 parts. ---- 260

240 parts. ---- x

==> Total amount (x) = (260*240)/32 = 1950

## Ques 8.

If the coin is to be tossed three times, what is the probability that on at least one of the tosses of the coin will turn up Tails ?

**Solution :**

1 - 1/8 = 7/8

## Ques 9.

If the income tax is increased by 19% the net income is reduced by 1%. The rate of income tax is?

**Solution :**

1/(19+1) x 100 =1/20 x100=5%

## Ques 10.

Asha got married 9yrs ago.today her age is 4/3 times her age at the time of marriage.at present her daughter's age is 1/6th of her age.wat was her daughter's age two yrs ago?

**Solution :**

x=4/3(x-9)

==>x=4/3x-12

==>12=1/3x

==>X=36

==>x=4/3x-12

==>12=1/3x

==>X=36

Daughter age = 36/6=6

Daughter age two years ago = 6-2=4

Daughter age two years ago = 6-2=4