Test: Arithmetic - 1 (2019-2019) - UPSC MCQ

Total marks of 100 students
= 40 × 100 = 4000
correct mean marks of 100 students

Let price of each mobile is ₹ 1000.
Then, Price of 8 mobile = ₹ 8000.
Price of 10 mobile = ₹ 10000.
Percentage discount = 

Mother is 24 years older then Ena.
So, at the time of Ena's birth, mother's age was 24 years.
Again, Ena was born after 4 years of their parents wedding
So, mother's age at the time of wedding = 24 – 4 = 20 years
Her father is 3 years older than her mother
So, her father's age at the time of their wedding = 20 + 3 = 23 years.

ATQ,

For (y – x) maximum, y should be maximum and x should be minimum.
(y – x) ≤ (40 – 25) 
∴ (y – x) ≤ 15.
Hence, (y – x) is away less then or equal to 15.

Let B's score is n and, A's score is (m)
ATQ,  m – n = 20

B's score = 400 – 20 = 380

Let the two-digit natural number are 10x + y on reversing its digits, number formed 10y + x
ATQ,

7(10x + y) = 4(10y + x)
70x + 7y = 40y + 4x
66x = 33y
2x = y
Hence, such number are (12, 24, 36, 48)

Percentage of members of the club went for shopping or Sighteeing 100 – 10 = 90%
1.  Percent of members went for both = 80 + 50 – 90 = 40%
2.  Percent of members went for only shopping = 80 – 40 = 40%
Hence, only statement 1 is true.

Number of non-Indian participants = 100 – 70 = 30.
1. Number of vegetarian = 60.      
Number of Indian that are vegetarian ≥ (60 – 30) ≥ 30
2. Number of non-vegetarian
= 100 – 60.
= 40.
Maximum Number of non-Indian that are non-vegetarian = 40 – 30 = 10
Hence, at least 10 Indian are non-vegetarian.

Cost of 10 balls + 10 rackets = 1300 + 1500 = 2800
∴ Cost of 1 ball + 1 racket = 280 ...(i)
ATQ,  Cost of 1 racket = 3 × Cost of 1 ball
∴ From (i)
Cost of 4 balls = 280
Cost of 1 ball   = 70
∴ Cost of 1 racket  = ₹ 210

Let Meera age in 2002 = x years
and Meenu age in 2002 = y years
∴ x = 3y and x + 8 = 2(y + 8)
⇒ 3y + 8 = 2y + 16 ⇒ y = 8
Meenu's age = 8 years
Hence, Meenu's year of birth = 2002 – 8 = 1994

Price of the mobile phone

After taking ₹ 2000 from his friend, Raju has 9000 + 2000 = ₹ 11000.
Thus, he still does not have enough amount to buy the handset.

L.C.M. of 4 and 6 = 12.
Hence the number assign to the students who play cricket as well as football is divisible by 12.
Number divisible by 12 are 12, 24, 36......
Total number of such Numbers up to 100 = 8. and that are 12, 24, 36, 48, 60, 72, 84, 96.
Hence required number = 8

Let weight of block A = x kg
and weight of block B = y kg
total weight of two blocks = (x + y) kg
ATQ, 

x + y = 1.6x ⇒  y = 0.6x.
Now, when block B is removed, then percent reduction in the weight

Number of times ‘5’ appear from 1 to 100 = 20
Number of times ‘5’ appear from 101 to 200 = 20
Similary, number of times ‘5’ appear from 201 to 499 = 60
Number of times '5' appear from ‘600 to 1000’ = 80
Number of times ‘5’ appear from ‘500 to 599’. = 120
Total number of times ‘5’ appear from 1 to 1000
= 20 + 20 + 60 + 80 + 120 = 300

'7 A3' is divisible by 3 only when sum of its digits be divisible by 3.
7 + A + 3 = 10 + A
For, A = 2, 5 and 8. (10 + A) would be divisible by 3.
ATQ,

for A = 2, B = 8,
136 + 587 = 723
Hence, B = 8

Let the sum of the weight of two childrens is x kg. and weight of mother and father are y and z kg respectively.
ATQ,

here, z = 60, (given)
from (ii)
x + 60 = 156
x = 96
From (i),
96 + y = 150
y = 150 – 96 = 54 kg.

Number of people who read either or both languages.
= 15 – 3 = 12.

∴ a + b + c = 12
Number of people who read French,
a + b = 7
Number of people read English,
b + c = 8
∴ (a + b) + (b + c) = 7 + 8 = 15
⇒ (a + b + c) + b = 15
⇒ 12 + b = 15 Þ b = 3
∴ a = 4 and c = 5
Hence, number of people who can read exactly one language
=  a + c = 9

In each hour clock moves fast by

Number of hours between 8:00 am on monday and 6:00 pm on wednesday
= 58 hours.
So, clock will move fast in  58 hours

So, current time
= 6 – 24.16 = 5:36 pm.

A number is divisible by '3' if sum of its digits be divisible by 3.
Here, Given number is 4252746 B
Sum of its digits = 4 + 2 + 5 + 2 + 7 + 4 + 6 + B
= 30 + B.
For, B = 0, 3, 6, 9;
Sum of digits will be divisible by '3'.
Hence, number of values of  B = 4.

Let first Piece, second Pieec and third Piece are x, y and z respectively.
Now 
According to question,


∴ The length of the original sheet
= x + y + z
= 5 + 10 + 15
= 30 units