The boys and the girls in a school are in the ratio 7 : 4. If total strength of the school be 550, find the number of boys and girls.
We have the ratio boys : girls = 7 : 4.
So, let there be 7x boys and 4x girls. It is given that there are a total of 550 students in the school.
Therefore, 7x + 4x = 550
11x = 550
x = 550/11 = 50
Hence, the number of boys = 7x = 7×× 50 = 350, and the number of girls = 4x = 4 ×× 50 = 200.
The ratio of monthly income to the savings of a family is 7 : 2. If the savings be of Rs 500, find the income and expenditure.
We have the ratio of income : savings = 7 : 2.
So, let the income be 7x and the savings be 2x. It is given that the savings are Rs 500.
Therefore, 2x = 500
x = Rs 500/2 = Rs 250
Thus, the income = 7x = 7 × 250 = Rs 1750.
Now, expenditure = Income − savings = Rs 1750 − Rs 500 = Rs 1250.
Thus, the income = Rs 1750, and the expenditure = Rs 1250.
The sides of a triangle are in the ratio 1 : 2 : 3. If the perimeter is 36 cm, find its sides.
We have the ratio of the sides of the triangle = 1 : 2 : 3.
Now, let the sides of the triangle be x, 2x and 3x, respectively.
Therefore, the perimeter = x + 2x + 3x = 36
⇒ 6x = 36
⇒ x = 36/6 = 6
Thus, the sides of the triangle = x = 6 cm; 2x = 2××6 = 12 cm; 3x = 3 ××6 = 18 cm.
So, the sides of the triangle = 6 cm, 12 cm and 18 cm.
A sum of Rs 5500 is to be divided between Raman and Aman in the ratio 2 : 3. How much will each get?
We have
Sum of the terms of the ratio = 2 + 3 = 5, and the total sum = Rs 5500
Therefore, Raman's share = (2/5×5500) = Rs 2200
Aman's share = (3/5×5500) = Rs 3300
The ratio of zinc and copper in an alloy is 7 : 9. If the weight of the copper in the alloy is 11.7 kg, find the weight of the zinc in the alloy.
We have
Weight of zinc : weight of copper = 7 : 9
So, let the weight of zinc in the alloy be '7x' kg and the weight of copper in the alloy be '9x' kg.
But the weight of copper in the alloy is given to be 11.7 kg.
Therefore, 9x = 11.7
x = 11.7/9 = 1.3
Hence, the weight of zinc in the alloy = 7x = 7××1.3 = 9.1 kg.
In the ratio 7 : 8, if the consequent is 40, what is the antecedent?
In a ratio a : b, 'a' is known as the antecedent and 'b' is known as the consequent.
In the given ratio, let the antecedent be 7x and the consequent be 8x, respectively,
But consequent = 8x = 40
x = 40/8 = 5
Therefore, the antecedent = 7x = 7××5 = 35.
Divide Rs 351 into two parts such that one may be to the other as 2 : 7.
We have
Sum of the ratio of the terms = 2 +7 = 9
Therefore, first part = Rs. (2/9×351) = Rs. 78
Similarly, second part = Rs. (7/9×351) = Rs. 273
Find the ratio of the price of pencil to that of ball pen, if pencils cost Rs 16 per score and ball pens cost Rs 8.40 per dozen.
We have
Cost of 1 score of pencils = Rs. 16
Since 1 score = 20 items,
Cost of one pencil = Rs. (16/20) = Rs. 0.8
Cost of 1 dozen ball pens = Rs. 8.40
Since 1 dozen =12 items,
Cost of one ball pen = Rs. (8.40/12) = Rs. 0.7
So, price of pencil : price of ball pen = 0.8 : 0.7 =0.8/0.7 = 8/7
Price of pencil : price of ball pen = 8 : 7
In a class, one out of every six students fails. If there are 42 students in the class, how many pass?
We have
One out of every six student fails, which means that 1/6th of the total students fail in the class.
And total number of students in the class = 42.
Therefore, the number of students who fail = (1/6× 42) = 7.
So, the number of students who pass = (Total students −the number of students who fail) = 42 − 7 = 35.
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