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1
The average height of the first six students is 170 cm, the average height of the last eight students is 175 cm. The average height of the total 16 students is 180 cm. Find the average height of the rest two students.
» Explain it
D
Sum of the heights of the first six students = 170 × 6 = 1020 cm

Sum of the heights of the last eight students = 175 × 8 = 1400 cm

Sum of the heights of the total 16 students = 180 × 16 = 2880

Sum of the height of the left 2 students = 2880 – 1020 – 1400 = 460

 Average height of the left 2 students = 460 = 230 cm 2

Hence, option D is correct.
2
The average salary of each trainee in an startup is Rs. 90. The average salary of 16 trainees is Rs.708.75 and the average salary of the rest is Rs. 75. How many trainees does the startup have?
» Explain it
B
Total salary of trainees = 16 × 708.75 = Rs. 11,340

Let there be x trainees.

∴ Total salary = Rs. (90x) and salary of remaining trainees = Rs. [75(x − 16)]

∴ 90x = 11340 + 75x − 1200

∴ 15x = 10140 i.e. x = 676

Hence, option B is correct.
3
In a hostel, food is available for 200 students for 50 days. After 10 days, 50 more students join the hostel. For how many more days will the food last?
» Explain it
B
Man days for which food is available = 200 × 50 = 10000

Available food is enough for 1 student for 10000 days

Food used by 200 students in 10 days = 200 × 10 man days of food = 2000

Man days of food left = 10000 – 2000 = 8000 man days of food

Total number of students now = 200 + 50 = 250

Remaining food can be used for 250 students for

 = 8000 days = 32 days 250

Hence, option B is correct.
4
The average weight of five friends P, Q, R, S, and T is (x + 6) kg while the average weight of R and T is (x – 6) kg. If the weight of another person U is also added, then average weight of all of them is reduced by 5 kg. Find the value of ‘x’ if average weight of P, Q, S and U is 94.5 kg.
» Explain it
D
Total weight of friends P, Q, R, S and T = (x + 6) x 5 = 5 (x + 6) kg

So, total weight of P, Q and S = 5 (x + 6) – 2 (x – 6) = (3x + 42) = 3 (x + 14)

Weight of U = (x + 6 – 5) × 6 – 5 (x + 6) = 6 (x + 1) – 5 (x + 6) = (x – 24) kg

According to the question,

[3 (x + 14) + (x – 24)] = 94.5 × 4

4x + 18 = 378

4x = 360; x = 90

Hence, option D is correct.
5
A, B, C, D and E are five persons. The weight of A, B and C is 90%, 112% and 94% respectively of the average weight of all five. The ratio of weight of D and E is 6 : 11. The difference between the weight of D and E is 75kg. What is the average weight of al the five persons?
» Explain it
E
Let the average weight of all five = 100k

So, weight of A = 90k, B = 112k and C = 94k

Let the weight of D = d and that of E = e

 90k + 112k + 94k + d + e = 100k 5

d + e = 204k

 d : e = 6 : 11 → d = 6 × 204 = 72k → e = 132k 17

Difference = 132k – 72k = 60k

60k = 75

 So, k = 75 = 1.25 60

Average weight of all the five persons = 100 × 1.25 = 125kg

Hence ,option E is correct.
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