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Directions: Study the following questions carefully and answer the questions given below.
1
The average of five numbers is 56. If the average of first four numbers is 54, what is the value of the fifth number ?
» Explain it
D
The sum of five numbers = 56 × 5 = 280

The sum of first four numbers = 54 × 4 = 216

∴  Fifth number = 280 – 216 = 64

Hence, option D is correct.

2
The average of six numbers is 20. If one number is removed, the average becomes 15. What is the number removed ?
» Explain it
D
Sum of six numbers = 6 × 20 = 120

Given that if one number is removed, the average becomes 15.

∴  Sum of five numbers = 5 × 15 = 75

Now,  required number = 120 – 75 = 45.

Hence, option D is correct.

3
Manish has a certain average for 11 innings. In the 12th innings he scores 120 runs and thereby increases his average by 5 runs. His new average is
» Explain it
C
To solve this question, we can apply short approach

Average after n innings = x – y(n – 1)

Where, x = 120;  y = 5;  n = 12 

∴  Required average = 120 – 5(12 – 1)

= 120 – 55  =  65 runs

Hence, option C is correct.

4
In a school with 600 students, the average age of the boys is 12 years and that of the girls is 11 years. If the average age of the school is 11 years and 9 months, then the number of girls in the school is
» Explain it
B
Let, the number of girls = x   &   the number of boys = (600 – x)

Given, the average age of the boys = 12 years

∴  Total age of the boys = 12(600 – x) years

And,  the average age of the girls = 11 years

∴  Total age of the boys = 11x years

Now,  average age of the school =  Total age of the boys + Total age of the girls
600

⇒  11 3  =  12(600 – x) + 11x
4 600

⇒   47  =  7200 – x
4 600

⇒  7200 – x = 7050

⇒  x = 7200 – 7050  =  150

Hence, option B is correct. 

5
A man purchases milk for three consecutive years. In the first year, he purchases milk at the rate of ₹ 7.50 per litre, in the second year, at the rate of ₹ 8.00 per litre and in the third year, at ₹ 8.50 per litre. If he purchases milk worth ₹ 4,080 each year, the average price of milk per litre for the three years is
» Explain it
B
Price of milk in first year = ₹ 7.50 per litre.

∴  Quantity of milk in first year =  4080  = 544 litres
7.50

Price of milk in second year = ₹ 8.00 per litre.

∴  Quantity of milk in second year =  4080  = 510 litres
8.00

Price of milk in third year = ₹ 8.50 per litre.

∴  Quantity of milk in third year =  4080  = 480 litres
8.50

∴  Required average =  3 × 4080  =  12240   =  ₹ 7.98
544 + 510 + 480 1534
 

Hence, option B is correct.