Quant Boosters  Maneesh  Set 2

100+Gain%/100 = True scale weight/False scale weight
Gain % = (100 * 1000/960) – 100 = 104.166  100 = 4.16%

Q21) A man purchases a certain number of oranges at 25 a rupee and same number at 20 a rupee. He mixes them together and sells them at 45 for two rupees. How much percent does he gain or lose in the transaction?

LCM (25,20,45) = 900
Cost price of 900 orange which is purchased 25 at a rupee = 900/25 = Rs.36
Cost price of 900 orange which is purchased at 20 a rupee = 900/20 = Rs.45
Selling price of 1800 oranges which is sold at 45 for two rupees = 1800 * 2/45 = Rs.80
Loss = 36+4580 = Rs.1
Loss % = 100/81 % = 1.23%

Q22) The cost price of 10 articles is equal to the selling price of 9 articles. Find the profit percent.

Let cost price of one article be Rs.1.
Cost price of 10 articles Rs.10
Selling price of 9 articles Rs.10
Selling price of 10 articles = 10 +10/9 = 100/9
Profit = 100/9  10 = 11.11 – 10 =Rs.1.11
Profit % = 1.11*100 / 10 = 11.11%

Q23) A trader allows two successive discounts of 20% and 15%. If he gets Rs.136 for an article, find its marked price.

Effective discount = (a+b(ab/100)) %
= 20+15300/100 = 353 = 32%
Marked price * 68/100 = 136
Marked Price = 136 * 100/68 = Rs.200

Q24) Two goods are sold at the same price one at a loss of 15% and other at a profit of 15%. Find the overall profit/loss.

Overall loss = (P^2/100) % = 225/100 = 2.25%

Q25) Selling an article for Rs.24, the profit percentage is equal to the cost price In rupees. Find the cost price of article.

24Cost Price/Cost price = Cost price/100
(Cost Price)^2 +100 * Cost price – 2400 = 0
(Cost price +120) * (Cost price20) = 0
Cost price = 120 or 20
Since price cannot take negative value , Cost price = Rs.20

Q26) At what time between 4 and 5 will the hands of a watch coincide?

At 4 o clock the hands are 20 minutes apart.
In order to coincide minute hand must gain 20 minutes.
Minute hand gains 55 minutes in 60 minutes.
Hence it will gain 20 minutes in > 60*20/55 = 240/11 = 21 9/11 minutes
Hence hands will coincide at 21 9/11 minutes past 4.

Q27) At what time between 4 and 5 will the hands of a watch point in opposite directions?

They will be in opposite direction when there is 30 minute space between them.
This will happen when minute hand gains 50 minutes (at 4 o clock hands are 20 minutes apart).
Minute hand gains 50 minutes in 60 * 50/55 = 600/11 =54 6/11 minutes.
Hence hands point in opposite directions at 54 6/11 past 4.

Q28) My watch which gains uniformly is 2 minutes slow at noon on Sunday and is 4 minutes 48 seconds fast at 2 p m on the following Sunday. When it was correct?

Sunday noon to next Sunday 2 PM = (24 * 7) + 2 = 170 hours
In 170 hours watch gains 2 + 4 + 48/60 minutes
In 170 hours watch gains 6 4/5 minutes.
Hence in order to gain 2 minute watch will take 170 * 5 * 2/34 = 50 hours
50 hours means 2 days and 2 hours.
That means at 2 PM on Tuesday it was correct.

Q29) From noon by how many degrees has the minute hand moved to 2:40 ?

One hour means minute hand moves 360 degree
2 hours means minute hand moves 720 degree
40 minute means minute hand moves 240 degree
Hence total = 720+240 = 960 degrees.How many degrees does an hour hand move in 20 minutes?
In one hour hour hand moves 30 degrees.
Hence in 20 minutes hour hand moves 30/3 = 10 degrees.

Q30) What is the angle between the minute hand and hour hand of a clock when the time is 7:30?