## Ques 1.

Pavan earned a profit of 50 percent on selling an article for Rs. 9000 . What was the cost price of the article?

**Solution :**

9000 ----- 150%

? ------ 100%

Cost Price = (9000*100)/150 = 6000

## Ques 2.

A, B and C start running around a circular stadium and complete one round in 10 seconds, 12 seconds and 16 seconds respectively. In how much time will they meet again at the starting point?

**Solution :**

**Take L.C.M of 10,12 and 16 = 240 seconds = 4 minutes**

## Ques 3.

I. 12 x² – 17 x + 6 = 0 II. 20 y² – 31 y + 12 = 0

**Solution :**

I. 12x2 – 17x + 6 = 0

==> 12x2– 9x – 8x + 6 = 0

==> 3x(4x – 3) – 2(4x – 3) = 0

==> (3x – 2) (4x – 3) = 0

==> 3x – 2 = 0

X= 2/3

==> 4x-3=0

==> x = 3/4

II. 20y2 – 31y + 12 = 0

==>20y2 – 16y – 15y + 12 = 0

==>4y(5y – 4) – 3(5y – 4) = 0

==> (4y – 3) (5y – 4) = 0

y = 3/4 and 4/5

Hence x < y

## Ques 4.

There are 3 red balls, 4 white and 6 yellow. Two balls are drawn at random. What is the probability that none is red?

**Solution:**

There are 10 balls other than red, and total 13 balls 2 balls are drawn, so Probability that none is red = 10C2 / 13C2

= 10*9/13*12 = 15/26

## Ques 5.

If the difference between the compound interest and the simple interest on a certain sum for 2 years at 8% p.a. is Rs. 32, then the sum is

**Solution :**

Sum = difference between interest *(100/r)^2

==> Sum = 32*(100/8)^2= 5000

## Ques 6.

The sum of the age of Father and his daughter is 62years. After 5 years, the age of father will be five times that of the son. What is the age of the Son ?

**Solution :**

Son = 62-5(5-1)/5+1 = 62-20/6 = 42/6 = 7

## Ques 7.

The ratio between two numbers is 7:5. If 5 is subtracted from each of them, the new ratio becomes 3:5. Find the numbers.

**Solution:**

(7x – 5)/(5x – 5) = 3/5

X = 1/2 so the numbers are 7/2 and 5/2

## Ques 8.

A rectangle garden having length and breadth as 110 m and 65 m respectively has 2.5 m wide path around the sides inside the garden. Find the cost of gravelling the path at 50 paise per sq. metre.

**Solution :**

Area of garden = 110*65 = 7150 m2

Area of path = (110-5)*(65-5) = 6300 m2

So area of path = 7150 – 6300 = 850 m2

So cost = 850*(50/100) = Rs 425

## Ques 9.

Complete the series : - 10, 52, 253, 1006, 3013, ?

**Solution :**

10*6 -8 = 52

52 *5 – 7 = 253

253 *4 – 6 = 1006

1006 *3 – 5 = 3013

3013 *2 – 4 = 6022

## Ques 10.

A person sell two horses for rupees 480 each. On the first horse he gains 25 percent and on the second horse he losses 25 percent. Find the percent gain or loss in the transaction.

**Solution :**

(25/10)^2 = 6.25% loss