AMCAT Averages Quiz-1

Explanation :
Total weight of the class X.
Acc. to Question:
X / 39 = 23
X= 897
Let Sarika garg and Tina dutta be 15y and 8y.
\frac{897-23y}{37}=23
897-851 = 23y
y = 2
Hence, Sarika’s age = 15 x 2 = 30
Tina’s age = 8 x 2 = 16

Explanation:
In 2010: 4x+72/4 = x+18
After death : 3x+36+3*\frac{N}{3} = x+18-3
N = 3 years
3x+36+3*\frac{N}{3} = (x+18)
N = 6 years
6-3 = 3 years from his death

First = 1.5x
Second = x
Third = 3x
Fourth = 1.5x
average = 24.5 = \frac{(1.5x+x+3x+1.5x)}{4}
x = 14

Total expenditure = 459x
36 students joined then total expenditure = 459x+81
average = 459x+81/495 = x-1
x = 16
original expenditure = 16*459 = 7344

Explanation:
Let the cost of Intel Laptop be x
As Apple is 70% higher than Intel, the cost of Apple = x + 0.7x = 1.7x
Excluding Intel and Apple, there are 30 Laptops with an average cost of Rs. 8880
Total cost of these 30 Laptops = 30 * 8880 = Rs. 266400
Total cost of all 32 Laptops = 32 * 9000 = Rs. 288000
Cost of Intel + Cost of Apple = Total cost of all Laptops - Total cost of 30 Laptops
x + 1.7x = 288000 - 266400
2.7x = 21600
x = 8000 (Cost of Intel)
Cost of Apple = 1.7x = 1.7 * 8000 = Rs. 13600

9*22 – 9*6/8 = 18

Explanation:
\frac{8000}{n} = a
\frac{8085}{n}+5 = a-1
n^{2} + 90n – 40000 = 0
n = 160
n^{2} + 5 = 165

Explanation:
Average weight = (Sum of weights)/(Number of people)
19=\frac{[(\frac{19}{2})\times (2a+18d)]}{19}
19\times 19=\frac{19}{2}\times(2a+18d)]
38= 2a+18d
The weight of the heaviest person is 37 kg.
So, a + 18d = 37
Solving these two equations, we get:
a = 1 kg

Explanation:
40*32 = 1280
1280-\frac{H}{39} = 31
H =71
1280-71- \frac{L}{38} = 31
L = 31

Explanation:
17X = \frac{17}{2} *(2a+16d)
X = a+8d
13Y = \frac{17}{2}*(2a+16d) – (4a+26d)
Y = a+8.46d