averages Model Questions & Answers, Practice Test for ssc cgl tier 1 2023

Question :1

The average weight of a group of 53 girls was calculated as 58 kgs. It was later discovered that the weight of one of the girls was read as 65 kgs., whereas her actual weight was 45 kgs. What is the actual average weight of the group of 53 girls? (rounded off to two digits after decimal)

Answer: (d)

Increase in weight

= 65 – 45 = 20 kg.

∴ Increase in average

= $20/53 = 0.38$

∴ Actual average weight

= 58 – 0.38 = 57.62

Question :2

One-third of a certain journey is covered at the rate of 25 km / hr, one-fourth at the rate of 30 km / hr and the rest at 50 km / hr. Find the average speed for the whole journey.

Answer: (b)

Let the total journey be x km.

Then $x/3$ km at the speed of 25 km/hr and $x/4$ km at 30 km/hr and the rest distance $(x - x/3 - x/4) = 5/12x$ at the speed of 50 km/hr.

Total time taken during the journey of x km

= $x/{3 × 25} hrs + x/{4 × 30} hrs + {5x}/{12 × 50}hrs$

= ${18x}/600 hrs = {3x}/100 $ hrs

∴ average speed = $x/{{18x}/600} = 100/3 = 33{1}/3$ km/hr

Question :3

A man’s age is 125% of what it was 10 years ago, but 83$1/3$% of what it will be after 10 years. What is his present age?

Answer: (b)

Let the present age be x yrs. Then

125% of (x – 10) = x; and 83$1/3$% 3 of (x + 10) = x

∴ 125% of (x – 10) = 83$1/3$% 3 of (x + 10)

$5/4(x = 10) = 5/6(x + 10)$

or, $5/4x - 5/6x = 50/6 + 50/4$

or, ${5x}/12 = 250/12$

∴ x = 50 yrs.

Question :4

Eleven years earlier the average age of a family of 4 members was 28 years Now the age of the same family with six members is yet the same, even when 2 children were born in this period. If they belong to the same parents and the age of the first child at the time of the birth of the younger child was same as there were total family members just after the birth of the youngest members of this family, then the present age of the youngest member of the family is

Answer: (c)

 No. of family membersAverageTotal
Eleven years earlier 428112
Presentlyif 439156
 628168

Since it is obvious that just after the birth of the youngest member (i.e., child) was 6 family members in the family.

Therefore at the time of the birth of the youngest child the elder child's age was 6 years.

Now the sum of their ages

= x + (x + 6) = 12 = (168 – 156)

⇒ x = 3

Question :5

A person covers half his journey by train at 60 kmph, the remainder half by bus at 30 kmph and the rest by cycle at 10 kmph. Find his average speed during the entire journey.

Answer: (b)

Recognise that the journey by bus and that by cycle are of equal distance.

Hence, we can use the short cut illustrated earlier to solve this part of the problem.

Using the process explained above, we get average speed of the second half of the journey as

10 + 1 × 5 = 15 kmph

Then we employ the same technique for the first part and get 15 + 1 × 9 = 24 kmph

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