Numbers Exercise 1

Quantity of wheat for 7 days = 112 kg

∴ Quantity of wheat for 1 day = kg

∴ Quantity of wheat for 69 days = × 69 = 1104 kg

Number of pieces = = 53

Required amount = = ₹1905

Lowest number of set A

= – 4 = 52

Lowest number of other set = 52 × 2 – 71 = 33

∴ Required sum = 33 + 34 + 35 + 36 + 37 = 175

of the number = 84

∴ number = = 105

Let the number be = x

According to the question,

⇒

⇒

∴ Highest number = 24 + 6 = 30

Let the smaller number be x

x (x + 2) = 5358

⇒ x² + 2x – 5328 = 0

⇒ (x + 74) (x – 42) = 0

∴ x = 72

From the given alternatives,

1763 = 43 × 41

According to the question,

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

Quicker Approach:

The unit’s digit of the number 16128 is 8.

From the given answer choices,

126 × 128 = 16128

∴ Required larger number = 128

Out of the given alternatives,

56 × 57 = 3192

Let the three consecutive integers be

x, x + 1 and x + 2

According to the question,

x + x + 1 + x + 2 = 39

⇒ 3x + 3 = 39

⇒ 3x = 39 – 3 = 36

⇒ x = = 12

∴ Required largest number

= x + 2 = 12 + 2 = 14

Let the smaller number be x

x × (x + 2) = 4488

⇒ x² + 2x – 4488 = 0

⇒ (x + 68) (x – 66) = 0

∴ x = 66

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

Out of the given alternatives,

137 × 139 = 19043

∴ Required smaller number = 137

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

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 + C = 146

⇒ A + A + 4 = 146

⇒ A =

∴ E = A + 8 = 71 + 8 = 79

Let the cost of one chair be ₹x and that of a table be = ₹y

According to the question,

3x + 10y = ₹9856

⇒ 2 × (3x + 10y) = 2 × 9856

∴ 6x + 20y = ₹19712

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.

Number of mangoes = 12 dozens

= 12 × 12 = 144

∴ Number of mangoes in 43 boxes

= 43 × 144 = 6192

Amount received by each student = = ≈ ₹204