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MathematicsClass 6CBSE

The cost of 10 tables is ₹ 7500. Find the number of tables that can be purchased with ₹ 9000.

Number of tables purchased in ₹ 7500 = 10Number of tables purchased in ₹ 1 =10/7500∴ Number of tables purchased in ₹ 9000=10×9000/75000=12

MathematicsClass 6CBSE

Are 20, 25, 12, 15 in proportion?

We have 20, 25, 12, 15Product of extremes = 20 × 15 = 300Product of middles = 25 × 12 = 300Since both the products are same.∴ The four numbers 20, 25, 12, 15 are in proportion.

MathematicsClass 6CBSE

Green paint is made by mixing blue, yellow and white paints in the ratio 2: 7: 1. How much blue paint is needed to make 64 litres of green paint?

Here, sum of ratios = 2 + 7 + 1 = 10∴ Total quantity of green paint = 64 litresQuantity of blue paint =2/10× 64 = 12.8 litresTherefore, the required blue paint = 12.8 litres.

MathematicsClass 6CBSE

Divide 60 in the ratio of 2: 3.

Sum = 2 + 3 = 5∴ First part =2/5 × 60 =24 5∴ Second part =3/5 × 60 =36 5Thus, the required two parts = 24 and 36.

MathematicsClass 6CBSE

Write True or False against the following statement:8: 9:: 24: 27.

24: 27 = 24/27=24÷3/27÷3 [∴H.C.F.(24, 27) = 3] = 8/9=8:98: 9 = 24: 27∴ 8: 9:: 24: 27 is true(T).

MathematicsClass 6CBSE

Are the following statement true? 45km: 60km = 12 hours: 15 hours.

45km: 60km =45/60 = 45÷15/60÷15 [∴ H.C.F.(45, 60) = 15] = 3/4 = 3: 412 hours: 15 hours =12/15=12÷3/15÷3 [∴H.C.F.(12, 15) = 3] =4/5=4:5Since, the two ratios are not equal, therefore the given statement is false(F).

MathematicsClass 6CBSE

The weight of 25 copies is 5 kg. Find the weight of 30 such copies?

It is given thatWeight of 25 copies = 5 kg∴ Weight of 1 copy = 5 ÷ 25 = 1/5kg∴ Weight of 30 copies = 30 x 1/5= 6 kg

MathematicsClass 6CBSE

If a = 2b then a: b = ____.

If a = 2b then a: b = 2: 1.

MathematicsClass 6CBSE

5: 4 = ____.

5: 4 = 30: 24.

MathematicsClass 6CBSE

32 m: 64 m:: ____.

32 m: 64 m:: 6 Sec: 12 Sec.

MathematicsClass 6CBSE

If 4, a, a, 36 are in proportion then a is equal to ____.

If 4, a, a, 36 are in proportion then a is equal to 12.

MathematicsClass 6CBSE

Anshika’s Score in Science is 15 more than the two-third of her score in Sanskrit. If she scores x marks in Sanskrit, find her score in Science.

Anshika’s score in Sanskrit = x∴ Her marks in Science = 2/3x + 15∴ Thus, Anshika’s score in Science = 2/3x + 15

MathematicsClass 6CBSE

A starts his car from Delhi at 6.00 am to Amritsar. The uniform speed of his car is x km/h. At 12.00 noon, he finds that he is still 50 km away from Amritsar. Find the distance between Delhi and Amritsar.

Time taken by A to reach Amritsar = 12.00 noon – 6.00 am = 6 hour.The uniform speed of the car = x km/ hr∴ Total distance covered by A = Time x speed = 6x km.∴ Distance between Delhi and Amritsar = (6x + 50) km

MathematicsClass 6CBSE

Think of a number, add 2 to it and then multiply the sum by 6, the result is 42.

Let the number be x.∴ Sum of x and 2 = x + 2Now by multiplying the sum by 6, we get6 × (x + 2) = 42⇒ 6 × x + 6 × 2 = 42⇒ 6x + 12 = 42By inspection, we get6 × 5 + 12 = 42⇒ 30 + 12 = 42∴ 42 = 42So, the required number = 5

MathematicsClass 6CBSE

If the side of an equilateral triangle is x, find its perimeter.

We know that the three sides of an equilateral triangle are equal.∴ x + x + x = 3x.Thus, the required perimeter = 3x units.

MathematicsClass 6CBSE

Think of a number x. Multiply it by 3 and add 5 to the product and subtract y subsequently. Find the resulting number.

Required number is (3x + 5)Now we have to subtract y from the result i.e., 3x + 5 – y

MathematicsClass 6CBSE

Write an algebraic expression for the following expressions:(a) The sum of a number x and 4 is doubled.(b) One fourth of a number x is added to one third of the same number.

(a) The required expression is 2 x (x + 4)(b) The required expression is 1/4 x +1/3 x

MathematicsClass 6CBSE

Write an algebraic expression for each of the following:(a) 3 subtracted from a number y.(b) 5 is added to three times a number x.

(a) The required expression is y – 3(b) The required expression is 5 + 3x

MathematicsClass 6CBSE

Six less than a number equals to two. What is the number?

Let the number be ‘x’.According to condition, we have x – 6 = 2By inspections, we have 8 – 6 = 2∴ x = 8Thus, the required number is 8.

MathematicsClass 6CBSE

Find the value of the expression 2x – 3y + 4z, if x = 10, y = -12 and z = 11.

Given expression = 2x – 3y + 4zIf x = 10, y = -12 and z = 11,The expression becomes, (2 × 10) (3 × -12) + (4 × 11)= 20 – (-36) + 44= 20 + 36 + 44= 100.

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