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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