Fractions | Maths Olympiad Class 6 PDF Download

Q1: Tarun initially possessed 3/4 kg of flour. After using 1/5 kg to prepare chapatti, how much flour remains?
(a) 1/4 kg
(b) 11/20 kg
(c) 1 x 1 / 4 kg
(d) 1/3 kg
Ans: (B)

• Tarun started with a total of 3/4 kg of flour.
• He utilized 1/5 kg for making chapatti.
• To find the remaining flour, we calculate: (3/4 - 1/5) kg.
• This simplifies to (15/20 - 4/20) kg, resulting in 11/20 kg left.

Q2: Karan spent half of his pocket money to buy a pair of shoes. He then used half of the remaining amount to purchase a book, and half of what was left to buy a study table. In the end, he had ₹ 350 left. How much money did he initially have?
(a) ₹ 4000
(b) ₹ 3000
(c) ₹ 2800
(d) ₹ 1080
Ans: (C)

• Let’s assume Karan started with ₹ x.
• He spent half on shoes, so he used ₹ x/2, leaving him with ₹ x/2.
• Next, he spent half of the remaining amount on a book, which is ₹ (x/2)/2 = ₹ x/4, leaving him with ₹ x/4.
• Then, he spent half of what was left on a study table, which is ₹ (x/4)/2 = ₹ x/8, leaving him with ₹ x/8.
• According to the problem, this remaining amount equals ₹ 350, so we set up the equation: ₹ x/8 = ₹ 350.
• Solving for x gives us x = ₹ 350 * 8 = ₹ 2800.

Q3: Vikas had 128 stickers. He gave 3/8 of his stickers to his father and 1/4 of his stickers to his brother. How many stickers does he have remaining?
(a) 50
(b) 65
(c) 80
(d) 48
Ans: (D)

• Total number of stickers Vikas had = 128
• Stickers given to his father = 3/8 × 128 = 48
• Stickers given to his brother = 1/4 × 128 = 32
• Stickers remaining = 128 – (48 + 32) = 128 – 80 = 48

Q4: Sudha cultivated tomatoes in half of her kitchen garden. She then planted spinach in one-fourth of the leftover are(a) What fraction of the garden is occupied by spinach?
(a) 1/2
(b) 1/3
(c) 1/8
(d) 1/6
Ans: (C)

• Let the entire garden be represented as x.
• The portion of the garden used for tomatoes is x / 2.
• The remaining area after planting tomatoes is x - x / 2 = x / 2.
• Spinach occupies one-fourth of this remaining area, which is 1/4 * (x / 2) = 1/8 of the total garden (x).

Q5: Four families went on a picnic, and each family brought a cake. If three-fourths of each cake was consumed, what is the total amount of cake eaten?
(a) 3 / 8
(b) 3
(c) 9 / 12
(d) 1
Ans: (B)

• Each cake had 3/4 of it eaten.
• There are 4 families, so we multiply the fraction eaten by the number of families.
• Total cake eaten = 4 x 3/4 = 3.
• Thus, the total amount of cake consumed is 3.