## Ques 1.

5, 14 , 40 , 117 , ?

**Solution :**

5*3-1 = 14

14*3-2 = 40

40*3-3 = 117

117*3-4 = 347

## Ques 2.

I. X2 = 1849 II. Y = (1849)^1/2

**Solution :**

**X = ±43**

Y = 43

x≤y

Y = 43

x≤y

## Ques 3.

P takes twice as much time as Q and thrice as much time as R to finish a piece of work. Working together they can finish the work in 6 days. R can do the work alone in ?

**Solution :**

**1/x+2/x+3/x = 1/6**

6/x = 1/6

x = 36

R = 3/x = 3/36 = 1/12 = 12 days6/x = 1/6

x = 36

R = 3/x = 3/36 = 1/12 = 12 days

## Ques 4.

1006.7+12328.98-5644.64 = 12543+ ?

**Solution :**
13335.68-5644.64 = 12543 + ?

7691.04 = 12543 + ?

? = 4851.96

7691.04 = 12543 + ?

? = 4851.96

## Ques 5.

A certain sum of money amounts to Rs.800 in 2 years and to Rs. 920 in 3 years then the is

**Solution :**

**==>(A2 – A1)/ T2-T1**

==>(920-800) /1 = 120

==>P = 800-240 = 560==>(920-800) /1 = 120

==>P = 800-240 = 560

## Ques 6.

Four years ago, the ratio of the ages of P and Q was 5 : 9. 8 years hence the ratio will be 2 : 3 respectively. Find the present age of Q?

**Solution :**
4years ago P:Q ration = 5:9 (Difference = 4)

8 years hence P:Q ratio = 2:3 ( Difference =1)

new ratios :

4 years ago = 5:9 *1 = 5:9

8 years hence = 2:3 *4 = 8:12

Difference in Q ratio = 12-9 = 3 units

3 units ----------- 12 years

12 units --------- ?

Q age 8 years hence = 48 years

Present age of Q = 48-8 = 40 years

## Ques 7.

The average age of P and Q 10 years ago was 20. The average age of P, Q and R today is 30, so what will be the age of R after 5 years.

**Solution :**

P+Q = 60.

P,R,Q = 90

so Age of Q = 30+5 = 35

P,R,Q = 90

so Age of Q = 30+5 = 35

## Ques 8.

The length and breadth of a rectangle are increased by 30% and 20% respectively. Its area will be increased by

**Solution :**

**30 + 20 + (30*20/100) = 56%**

## Ques 9.

Milk contains 20% water. What quantity of pure milk should be added to 50 liters of milk to reduce the quantity of water to 12% ?

**Solution :**

Pure Milk in 50 liters milk = 80*50/100 = 40

Water in 50 liters milk = 20*50/100 = 10

==> (40+x) / 10 = 88/12 = 22/3

==>3*( 40+x) = 220

==> 120+3x =220

==> X = 100/3 = 33.33

==> X = 100/3 = 33.33

## Ques 10.

P,Q and R shared the profit in a business in the ratio 5:7:8 and partnered for 14 months, 8 months and 7 months. Ratio of their investments is

**Solution :**

**Rs. x for 14 months, Rs. y for 8 months and Rs. z for 7 months**

==> 14x : 8y : 7z = 5 : 7 : 8

==> 14x/8y = 5/7

==> y = (49/20)x

==> 14x : 8y : 7z = 5 : 7 : 8

==> 14x/8y = 5/7

==> y = (49/20)x

**14x/7z = 5/8**

==>z = (16/5)x

==>z = (16/5)x

x:y:z = x:(49/20)x:(16/5)x

20:49:64

x:y:z = x:(49/20)x:(16/5)x

20:49:64