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QUESTION: 1

If a – b : b – c : c – d = 1 : 2 : 3, then what is the ratio of (a + d) : c?

Solution:

Let a – b = x, b – c = 2x and c – d = 3x

∴ c = 3x + d

b = 2x + c = 5x + d

a = x + b = 6x + d

a + d / c = 6x + d + d / (3x + d) = 2 / 1

QUESTION: 2

The average age of a family of 5 members is 20 years. If the age of the youngest member is 5 years, what was the average age of the family at the birth of the youngest member?

Solution:

Total age(at present) = 5 X 20 = 100 years.

Total age of the family excluding the youngest member (for the remaining 5 people) = 100 –5 = 95.

The average age of the other 4 people in the family = 95 / 4 years.

5 years ago their average age = 95 / 4 – 5 = 75 / 4 = 18.75 years

QUESTION: 3

The mean temperature of Monday to Wednesday was 35 °C and of Tuesday to Thursday was 30 °C. If the temperature on Thursday was 1/2 that of Monday, the temperature on Thursday was

Solution:

Monday + Tuesday + Wednesday = 3 X 35 = 105; Tuesday + Wednesday + Thursday = 3 X 30 = 90. Thus, Monday – Thursday = 15 and Thursday = Monday / 2 -> Monday = 30 and Thursday = 15

QUESTION: 4

The average of a batsman after 25 innings was 56 runs per innings. If after the 26th inning his average increased by 2 runs, then what was his score in the 26th inning?

Solution:

Normal process:

Runs in 26th inning = Runs total after 26 innings – Runs total after 25 innings

= 26 X 58 – 25 X 56

For mental calculation use: (56 + 2) X 26 – 56 X 25 )

= 2 X 26 + (56 X 26 – 56 X 25)

= 52 + 56 = 108

Since the average increases by 2 runs per innings, it is equivalent to 2 runs being added to each score in the first 25 innings. Now, since these runs can only be added by the runs scored in the 26th inning, the score in the 26th inning must be 25 X 2 = 50 runs higher than the average after 26 innings (i.e. new average = 58).

Hence, runs scored in 26th inning = New Average + Old innings X Change in average

= 58 + 25 X 2 = 108

QUESTION: 5

The average weight of 3 boys Ross, Joey and Chandler is 74 kg. Another boy David joins the group and the average now becomes 70 kg. If another boy Eric, whose weight is 3 kg more than that of David, replaces Ross then the average weight of Joey, Chandler, David and Eric becomes 75 kg. The weight of Ross is

Solution:

David's Weight = 4 X 70 – 3 X 74 = 280 – 222 = 58.

Eric’s weight = 58 + 3 = 61.

Now, we know that Ross + Joey + Chandler + David = 4 X 70 = 280 and Joey + Chandler + David + Eric = 75 X 4 = 300. Hence, Ross’s weight is 20 kg less than Eric’s weight. Ross = 61 - 20 = 41 kg.

QUESTION: 6

The average marks of a group of 20 students on a test is reduced by 4 when the topper who scored 90 marks is replaced by a new student. How many marks did the new student have?

Solution:

Let initial average be x.

Then the initial total is 20x

New average will be (x – 4) and the new total will be

20(x – 4) = 20x – 80.

The reduction of 80 is created by the replacement. Hence, the new student has 80 marks less than the student he replaces. Hence, he must have scored 10 marks.

Short Cut The replacement has the effect of reducing the average marks for each of the 20 students by 4. Hence, the replacement must be 20 X 4 = 80 marks below the original.

Hence, answer = 10 marks.

QUESTION: 7

The average age of a group of men is increased by 6 years when a person aged 26 years is replaced by a new person of aged 56 years. How many men are there in the group?

Solution:

When a person aged 26 years, is replaced by a person aged 56 years, the total age of the group goes up by 30 years. Since this leads to an increase in the average by 6 years, it means that there are 30 / 6 = 5 persons in the group.

QUESTION: 8

The average weight of 10 men is decreased by 2 kg when one of them weighing 140 kg is replaced by another person. Find the weight of the new person.

Solution:

The decrease in weight would be 20kgs (10people’s average weight drops by 2 kgs). Hence, the new person’s weight = 140 - 20 = 120.

QUESTION: 9

The average of the first ten composite numbers is

Solution:

Required average=(4 + 6 + 8 + 9 + 10 + 12 + 14 + 15 + 16 + 18) / 10 = 112 / 10 = 11.2.

QUESTION: 10

The average of 15 numbers is 18. If each number is multiplied by 9, then the average of the new set of numbers is

Solution:

When we multiply each number by 9, the average would also get multiplied by 9.

Hence, the new average = 18 X 9 = 162.

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