**Problem 1 : **

A fruit merchant bought mangoes in bulk. He sold 5/8 of the mangoes. 1/16 of the mangoes were spoiled. 300 mangoes remained with him. How many mangoes did he buy?

(A) 240 mangoes (B) 160 mangoes (C) 960 mangoes

**Solution :**

Let x be the number of mangoes he bought.

Then,

Number of mangoes sold = 5x/8

Number of mangoes spoiled = x/16

Number of mangoes remaining = 300

Total no. of mangoes -(no. of mangoes sold + no. of mangoes spoiled) = no. of mangoes remaining

Then, we have

x - (5x/8 + x/16) = 300

x - (10x/16 + x/16) = 300

x -11x/16 = 300

16x/16 - 11x/16 = 300

5x/16 = 300

Multiply each side by 16/5.

x = 300 ⋅ 16/5

x = (300 ⋅ 16) / 5

x = (60 ⋅ 16) / 1

x = 960

So, the fruit merchant bought 960 mangoes.

**Problem 2 :**

A family requires 2 1/2 liters of milk per day. How much milk would family require in a month of 31 days?

(A) 77 ½ liters (B) 65 ½ liters (C) 61 ½ liters

**Solution :**

Milk required for a day = 2 1/2 liters.

Then, the amount of milk (in liters) required for 31 days is

= 31 ⋅ 2 1/2

= 31 ⋅ 5/2

= (31 ⋅ 5) / 2

= 155/2

= 77 1/2

So, the family requires 77 1/2 liters of milk for 31 days.

**Problem 3 :**

A ream of paper weighs 12 1/2 kg. What is the weight per quire ?

(A) 5/8 kg (B) 3/8 kg (C) 1/2 kg

**Solution :**

Weight of 1 ream of paper = 12 1/2 kg

1 ream = 20 quires

Then, the weight of 1 quire is

= 12 1/2 ÷ 20

= 25/2 ÷ 20

= 25/2 ÷ 20/1

= 25/2 ⋅ 1/20

= (25 ⋅ 1) / (2 ⋅ 20)

= (5 ⋅ 1) / (2 ⋅ 4)

= 5/8

So, the weight of 1 quire of paper is 5/8 kg.

**Problem 4 :**

It was Richard's birthday. He distributed 6 kg of candies to his friends. If he had given 1/8 kg of candies to each friend, how many friends were there ?

(A) 36 Friends (B) 48 Friends (C) 96 Friends

**Solution :**

Total quantity of candies = 6 kg

Share of each person = 1/8 kg

Then, number of friends is

= 6 ÷ 1/8

= 6 ⋅ 8/1

= (6 ⋅ 8) / 1

= 48

So, there were 48 friends.

**Problem 5 :**

6 students went on a picnic.One student agreed to bear half of the expenses. The remaining 5 students shared the remaining expenses equally. What fraction of the expenses does each of 5 students pay?

(A) x/10 (B) x/ 5 (C) x/2

**Solution :**

Let x be the expense

Expense beared by one student = x/2

Remaining expense = x/2

Expense shared by the other 5 students = (x/2)/5

= x/10

**Problem 6 :**

I have 2 ½ times money that David has. If i have $100, how much money does David have?

(A) $50 (B) $70 (C) $40

**Solution :**

Let x be the amount that David has, then i will have

(2 1/2) ⋅ x.

That is 5x/2.

5x/2 = 100

5x = 200

x = 40

So, the amount that David has is $40.

**Problem 7 :**

In a basket there are two kinds of sweet packets. There are 7 packets of the first kind each weighing 1 ¼ kg and 9 packets of the second kind each weighing ¾ . What is the total weight of the sweets in the basket?

(A) 15 ½ kg (B) 12 ½ kg (C) 10 ½ kg

**Solution :**

Weight of first kind sweet = 1 1/4 kg = 5/4

Weight of second kind sweet = 3/4 kg

Total weight = 7 ⋅ (5/4) + 9 ⋅ (3/4)

= (35/4) + (27/4)

= 62/4

= 31/2

By changing the mixed fraction into improper number, we get 15 1/2 kg.

**Problem 8 :**

How many half-liter bottles can be filled from a can containing 37 ½ liter of milk?

(A) 77 bottles (B) 65 bottles (C) 75 bottles

**Solution :**

Quantity of milk = 37 1/2 = 65/2

Number of half liter bottles can be filled

= (65/2) / (1/2)

= (65/2) ⋅ (2/1)

= 65 bottles

**Problem 9 :**

A gentleman bought 200 liter of milk for a function. 4/5 of it was used for preparing sweets. 3/4 of the remaining milk was used for preparing coffee. How much of the milk remained ?

(A) 5 liter (B) 11 liter (C) 10 liter

**Solution :**

Original quantity of milk = 200 liter

Quantity of milk used for preparing sweets

= (4/5) of 200

= (4/5) ⋅ 200

= 160

Remaining quantity of milk = 200 - 160 ==> 40 liter

Quantity of milk used for coffee = (3/4) of 40

= (3/4) ⋅ 40

= 30 liter

Remaining quantity of milk at the end = 40 - 30

= 10 liters

**Problem 10 :**

Two thirds of a tank can be filled in 18 minutes. How many minutes will it require to fill the whole tank?

(A) 24 minutes (B) 16 minutes (C) 27 minutes

**Solution :**

Let x be the capacity of the tank.

Part of tank filed in 18 minutes = 2/3 of x

Part of tank to be filled = 1/3 of x

1/3 of x = 9 minutes

Time taken to fill the whole tank = 18 + 9

= 27 minutes

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