Olympiad Test: Mathematical Reasoning - 1 - Class 7 MCQ

Let Ravi gets x sums correct.
∴ Wrong sums = 2x
Now x  + 2x = 96 ⇒ 3x = 96.

From 1 to 100, there are ten numbers with 7 as unit’s digit –
7, 17, 27, 37, 47, 57, 67, 77, 87,97.
And ten number with 7 as ten’s digit –
70, 71, 72, 73,74, 75, 76, 77, 78, 79. 
Required number = 10 + 10 = 20

∵ 100 workers finish a work in 100 days 
∴ 1 worker finish a work in 100 × 100
∴ 40 workers finish a work = 
= 250 days

⇒ x² + 4x – 96 = 0
⇒ x² + 12x – 8x – 96 = 0
⇒ x(x + 12) – 8 (x + 12) = 0
⇒ (x – 8) (x + 12) = 0 ( ∵x ≠ – 12) 
⇒ x – 8 = 0 ⇒ x = 8

Let the number of women = x
Then number of men = 2x
In city B,
2x – 10 = x + 5 
⇒ 2x – x = 5 + 10 
⇒ x = 15
Total number of passengers in the beginning
= x  + 2x = 3x = 3 × 15 = 45 

Smallest no. of ducks = 3 

Seven strike of ducks = 3 intervals.
10 strikes have 9 intervals.
∵ 6 intervals have 7 sec and
∴ 1 interval have 7/6 second
∴ 9 intervals have 

Total ages of three persons = 86 years
Total ages of three persons after 2 years
= 86 + 2 + 2 + 2
= 92 years 

Let the number of keepers be x.
A/Q, Total number of feet
= total no. of heads + 224
⇒ 50 × 2 + 45 × 4 + 8 × 4 + 2 × x
= 50 + 45 + 8 + x + 224
⇒ 100 + 180 + 32 + 2x = 327 + x
⇒ 312 + 2x = 327 + x
⇒ 2x – x = 327 – 312 
⇒ x = 15 

Number of students who did not pass
= 450 – 270 = 180

Here,  x + 13x = 112

Let d be the daughter and s be the son.
d – 1 = s ⇒ d – s = 1 ….(1)
2 (s – 1) = d ⇒ 2s – d = 2 …..(2)
From (1) and (2)
– s  + d = 1
2s – d = 2
__________
Adding s = 3 

Total ages of 3 persons = 96.
Three years ago, total age of 3 persons
= 96 – 3 – 3 – 3
= 96 – 9 = 87 years 

Let son’s age be x.
Mr. Sharma’s age = 3x.
A/Q, 3x – 5 = 4 (x – 5)
⇒ 3x – 5 = 4x – 20 
⇒ 4x – 3x = – 5 + 20 
⇒ x = 15
Age of Mr. Sharma = 3x = 3 × 15 = 45 years. 

Speed of train = 72 km/hr.