Simplification with Explanation

Q1. Rakesh purchases a certain number of cookies for Rs. 400. If the price of a cookie is cheaper by Rs. 2 then he could have purchased 10 more cookies. Find the number of cookies purchased?

Answer- Option A

Explanation-

Let the number of cookies purchased be x and the price of a cookie be Rs. y
Then, xy = 400 ... (i)
(x + 10)(y - 2) = 400
(x + 10)

400 x

- 2

= 400

(x + 10)(200 - x) = 200x
x² + 10x - 2000 = 0
(x + 50)(x - 40) = 0
x = 40

Q2. The cost of 8 mangoes is equal to 5 pineapples, and the price of 6 pineapples is equal to 9 pomegranates. If 3 pomegranates cost Rs. 90, what is the price of a mango?

Answer- Option D

Explanation-

Given, 8 mangoes = 5 pineapples
6 pineapples = 9 pomegranates
3 pomegranates = Rs. 90
1 pomegranate = Rs. 30
1 pineapple =

9 6

x30 = Rs. 45

1 mango =

5 8

x45 = Rs. 28.125

Q3. In a city, the fare of a cab consist of fixed charge plus the charge for the distance covered. For a journey of 8 km, the charges paid is Rs. 300 and for 15 km, the charges paid is Rs. 335. Determine the charge a person will have to pay for 24 km?

Q4. In a class of 80 students, each girl donated rupees equal to the number of boys and each boy donated rupees equal to the number of girls. If the donation collected is Rs. 3000. How many girls are there in a class?

Answer- Option B

Explanation-

Let the number of girls be x. Then, the number of boys = 80 - x
x(80 - x) + (80 - x)x = 3000
x² - 80x + 1500 = 0
(x - 50)(x - 30) = 0
x = 50 or 30

Q5. A farmer has some cows and parrots. The number of legs is 20 more than twice the number of heads. How many cows are there with the farmer?

Answer- Option C

Explanation-

Let the number of cows be x and the number of parrots be y.
Then, 4x + 2y = 20 + 2(x + y)
2x = 20
x = 10

Q6. The cost of a piece of fabric is Rs. 80. If each meter costs Rs. 2 less then in the same price 2 meters more fabric would have been purchased. How long is the cloth?

Answer- Option A

Explanation-

Let the cost of a meter fabric be Rs.x and length of the fabric be y meter.
Then, xy = 80 and (x - 2)(y + 2) = 80

80 y

- 2

(y + 2) = 80

y² + 2y - 160 = 0
(y + 10)(y - 8) = 0
y = 8m

Q7. Suresh and Mahesh donated Rs. 100 each in charity. Mahesh gives each Rs. 1 more than Suresh and Suresh distributes money to 5 more people than Mahesh. How many people are there in this charity?

Answer- Option D

Explanation-

Let, Mahesh and Suresh donate money to x and (x + 5) people respectively.
Then,

100 x

-

100 x + 5

= 1

x² + 5x - 500 = 0
(x - 20)(x + 25) = 0
x = 20
Total number of people in the charity = x + (x + 5) = 45