Numbers 1
A canteen requires 112 kgs of wheat for one week. How many kgs of wheat will it require for 69 days?
Quantity of wheat for 7 days = 112 kg
∴ Quantity of wheat for 1 day = kg
∴ Quantity of wheat for 69 days = × 69 = 1104 kg
How many pieces of 8.6 metres length cloth can be cut out of a length of 455.8 metres cloth?
Number of pieces = = 53
If an amount of ₹41,910 is distributed equally amongst 22 persons, how much amount would each person get?
Required amount = = ₹1905
The sum of five consecutive even numbers of set A is 280. What is the sum of a different set B of five consecutive numbers whose lowest number is 71 less than double the lowest number of set A?
Lowest number of set A
= – 4 = 52
Lowest number of other set = 52 × 2 – 71 = 33
∴ Required sum = 33 + 34 + 35 + 36 + 37 = 175
The difference between a number and one fifth of it is 84. What is the number?
of the number = 84
∴ number = = 105
If the difference between a number and two fifths of the number is 30, find the number.
Let the number be = x
According to the question,
⇒
The average of four consecutive even numbers is 27. What is the highest number?
∴ Highest number = 24 + 6 = 30
The product of two consecutive even numbers is 5328. What is the smaller number?
Let the smaller number be x
x (x + 2) = 5358
⇒ x² + 2x – 5328 = 0
⇒ (x + 74) (x – 42) = 0
∴ x = 72
The product of two consecutive odd numbers is 1763. What is the larger number?
From the given alternatives,
1763 = 43 × 41
The sum of a set of five consecutive even numbers is 140. What is the sum of the next set of five consecutive even numbers?
x + x + 2 + x + 4 + x + 6 + x + 8 = 140
⇒ 5x + 20 = 140
⇒ 5x = 120
∴ x = = 24
∴ x + 8 = 24 + 8 = 32
The next set of five consecutive even number will start with = 34
∴ Required sum
= 34 + 36 + 38 + 40 + 42 = 190
The product of two consecutive even numbers is 16128. Which is the larger number?
Quicker Approach:
The unit’s digit of the number 16128 is 8.
From the given answer choices,
126 × 128 = 16128
∴ Required larger number = 128
The product of two successive numbers is 3192. What is the smaller number?
Out of the given alternatives,
56 × 57 = 3192
The sum of three consecutive integers is 39. Which of the following is the largest among the three?
Let the three consecutive integers be
x, x + 1 and x + 2
x + x + 1 + x + 2 = 39
⇒ 3x + 3 = 39
⇒ 3x = 39 – 3 = 36
⇒ x = = 12
∴ Required largest number
= x + 2 = 12 + 2 = 14
The product of two consecutive even numbers is 4488. Which is the smaller number?
x × (x + 2) = 4488
⇒ x² + 2x – 4488 = 0
⇒ (x + 68) (x – 66) = 0
∴ x = 66
The product of two successive numbers is 8556. What is the smaller number?
Let the number be x and (x + 1).
∴ x(x + 1) = 8556
⇒ x² + x – 8556 = 0
⇒ x² + 93x – 92 x – 8556 = 0
⇒ (x² + 93) (x – 92) = 0
∴ x = 92
The product of two consecutive odd numbers is 19043. Which is the smaller number?
137 × 139 = 19043
∴ Required smaller number = 137
The sum of the squares of two consecutive even numbers is 6500. Which is the smaller number?
Let the two numbers be x and (x + 2).
Then, x² + (x + 2)² = 6500
⇒ x² + x² + 4x + 4 = 6500
⇒ 2x² + 4x – 6496 = 0
⇒ x² + 2x – 3248 = 0
⇒ x² + 58x – 56x – 3248 = 0
⇒ (x + 58) (x – 56) = 0
⇒ x = 56
The product of two consecutive even numbers is 582168. Which is the smaller number?
Let the numbers be x and (x + 2)
Then, x × (x + 2) = 582168
⇒ x² + 2x – 582168 = 0
⇒ x² + 764x – 762x – 582168 = 0
⇒ (x + 764) (x – 762) = 0
⇒ x = 762
A, B, C, D and E are five consecutive odd numbers The sum of A and C is 146. What is the value of E?
A + C = 146
⇒ A + A + 4 = 146
⇒ A =
∴ E = A + 8 = 71 + 8 = 79
The cost of 3 chairs and 10 tables is ₹9856. What is the cost of 6 chairs and 20 tables?
Let the cost of one chair be ₹x and that of a table be = ₹y
3x + 10y = ₹9856
⇒ 2 × (3x + 10y) = 2 × 9856
∴ 6x + 20y = ₹19712
A canteen requires 13 dozen bananas per day. How many bananas will it require for 9 weeks?
Requirement of bananas for 1 day in the canteen = 13 dozens
∴ Requirement of bananas for 9 weeks i.e. 63 days
= 63 × 13 dozens
= 63 × 13 × 12 = 9828.
There are 12 dozen mangoes in a box. If there are 43 such boxes, how many mangoes are there in all the boxes together?
Number of mangoes = 12 dozens
= 12 × 12 = 144
∴ Number of mangoes in 43 boxes
= 43 × 144 = 6192
If an amount of ₹15,487 is divided equally among 76 students, approximately how much amount will each student get?
Amount received by each student = = ≈ ₹204
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