Q.1 In an examination, the number of those who passed and the number of those who failed were in the ratio 5 : 2. Had 25 more appeared, and 5 less passed, the ratio of passed to failed would have been 3 : 2. Find the number of candidates who appeared, initially.
Number of those who passed to number of those failed = 5 : 2
Let number of students who passed = 5x
and number of students who failed = 2x
Total number of students = 5x + 2x = 7x
When 25 more students appeared then total students = 7x + 25
When students increased, 5 less passed
Now number of students passed = 5x – 5
Number of students who failed = (7x + 25) – (5x – 5)
= 7x + 25 – 5x + 5 = 2x + 30
New ratio of passed to failure = 3 : 2
According to question
? 2 (5x – 5) = 3 (2x + 30)
10x – 10 = 6x + 90
? 10x – 6x = 90 + 10
4x = 100, x = 25
Hence number of students who appeared = 7 × 25 = 175.
Q.2 Two friends A and B have a certain amount of money in the ratio 2 : 3. If A gives Rs. 20 to B, the ratio will become 7 : 13. If B gives Rs. 20 to A, what will be the ratio of the money with A and B?
A) 4 : 5
B) 3 : 4
C) 9 : 11
D) 2 : 3
Assume 2k and 3k to be the money with A and B.
If A gives Rs. 20 to B the ratio will become = 2K-20 / 3K+20 = 7/13
If B gives Rs. 20 to A, the ratio will be = 2K+20 / 3K-20 = 9/11
Q.3 In a market in Lucknow, the price of a bag of 8 Oranges was Rs. 180/-. On the same day in Ludhiana a market was selling 5 Oranges for Rs. 100/-. A 3 bag was priced at Rs. 380/- in Chennai that day. In Bangalore Oranges were selling for Rs. 230 a dozen. The Oranges each weighed 150g. Where were the Oranges Cheapest ?
weight of 8 Oranges = 1.2kg
cost of 1.2 kg = Rs.180
cost of 1 kg Oranges = Rs.150
weight of 5 Oranges = 0.75kg
cost of 0.75 kg = Rs.100
cost of 1 kg = Rs.133.33
cost of 3kg Oranges = Rs.380
cost of 1 kg Oranges = Rs.126.66
weight of 12 Oranges = 1.8 kg
cost of 1.8kg Oranges = Rs.230
cost of 1 kg Oranges = Rs.127.77
from the above solution, it is clear that the Oranges were cheapest in Chennai
Q.4 In a row of students Sonam is eighth from the right & Rahul is sixteenth from the right. How many boys are there in a row?
D) Data inadequate
Since there are Total no. of students are not present
Q.5 A man is facing northwest. He turns 90 degrees in the clockwise direction and then 135degrees in the anti-clockwise direction. Which direction is he facing now?
Man is facing north-west direction.
He turns 90 degree in the clockwise direction and then 135 degrees in the anti-clockwise direction
So, net movement = 135-90 = 45 degrees in the anti-clockwise direction
45 degrees in the anti-clockwise direction from north-west = WEST
So, the man is facing west