Puzzle: 213                                                                                                                16.07.2018

Suresh and Mahesh took turns driving on a trip to Chennai and back. Suresh drove the first 40 kms and Mahesh the rest of the way to Chennai. On the way back Suresh stared to drive and Mahesh drove the last 50 kms. Which of the two drove most and how more did he drive?

The answer for puzzle-212: July 12

Solution for puzzle-212:

Total cars purchased in 2 weeks =  5* 14*2 =140

First day he sells 6 cars and buys 2 cars – net sale = 4 cars

Second day he sells 6 cars and buys 2 cars – net sale = 4 cars

Third  day he sells 5 cars and buys 3 cars – net sale = 2 cars

For a cycle of 3 days net sale = 10 cars

Since he was having in hand already 140cars, it would take 14 cycles of 3 days to bring the balance to zero. But it is not so.

Normally in these type of problems, we have to calculate the balance for the last but one cycle and then proceed day by day.

At the end of 13^th cycle ie., at the end of 39^th day, he would have sold 130 cars out 140cars and will be having in hand 10 cars.

Now on 40^th day he sells 6 cars and buys 2 cars

So at the end of 40^th day he will be having 6 cars in hand

On 41^st day he will sell 6 cars and buy 2 cars.

Since he is having only 6 cars in hand at the end of 40^th day, as soon as he sells 6 cars on 41^st day,  he will not be having any car in hand.

So on 41^st day he will shut down his business.

Commencing from June 2, if you calculate 41^st day, it will be July 12.

Puzzle: 212                                                                                                                 14.07.2018

Suresh likes to buy and sell cars. For two weeks he bought 5 cars for every 12 hours. Then on June 2^nd, he decided to start selling. On first and second days he would sell 6 cars and buy 2 cars. Third day he would sell 5 cars and buy 3. He decided to shut down his business when he has no more cars. At this rate on which date will be shut down his business?

The answer for puzzle-211: 2.828 lit

Solution for puzzle-211:

The volume of small box is 1 lit = 1000cc

Since the box is cubical, the length, width and height are the same which is 10cm

When this box is placed inside a cylinder perfectly, the diagonal of the sides of the small box will be the diameter of the cylinder.

The diagonal length  =10  

The diameter of the cylinder  = 10

When this cylinder is perfectly fitted into a bigger box, the diameter of the cylinder will be the side of the bigger box.

Side of the bigger box=10

Volume of the bigger box = 10

                                                = 1000*2  = 2000

                                                =2000 * 1.414 = 2828cc = 2.828 lit

Puzzle: 211                                                                                                                 13.07.2018

A box in the shape of a perfect cube with a volume of 1 lit is placed inside a cylinder. The dimensions of the cylinder is such that the box fits exactly inside it. The cylinder is then placed inside a larger cubical box. Again it is perfectly fit. What is the volume of the larger box? (Ignore the thicknesses of walls of small box and cylinder)

The answer for puzzle-210: 220 kg

Solution for puzzle-210:

               Let x be the weight of sugar sold with 6% profit.

Then (550-x) is the weight of sugar sold with 4% loss

Let y be the cost of sugar per kg

xy (1.06) + (550-x) 0.96y = 550y(1.02)

1.06 xy + ( 550 * 0.96y) – 0.96xy = 550(1.02)y

Cancelling y throughout,

1.06x + 528- 0.96x = 561

0.1x = 561-528= 33

X=330

The weight of sugar sold at 6% profit is 330kg

The weight of sugar sold at 4% loss is (550-330) = 220kg

Puzzle: 210                                                                                                                12.07.2018

A sugar merchant has 550 kg of sugar, part of which he sells at 6% profit and the rest at 4% loss. He gains 2% on the whole. What are the quantities he sold for 6% profit and 4% loss?

The answer for puzzle-209: Mohan will win by 1m

Solution for puzzle-209:

               Mohan runs 100m , Kumar runs 90m                                        

That means Kumar’s speed is 0.9 of Mohan’s speed.

In second case, Mohan runs 110m

Then Kumar will run (110*0.9) = 99m

Ie. When Mohan touches the finishing point, Kumar will be touching 99^th meter only.

So Mohan will win the race by 1m

Puzzle: 209                                                                                                                 11.07.2018

Mohan and Kumar race each other in a 100m race. Mohan wins by 10m. They decide to race again, but to make thing fair, Mohan starts 10m behind Kumar making the distance for Mohan as 110m. If they both run exactly the same speed as before, who will win the race?

The answer for puzzle-208: 15 days

Solution for puzzle-208:

Let the amount spent on each day be x

and the no.of days stayed be d.

xd=42000 ----(1)

If the amount spent is Rs.700 less, the no.of days stayed will be 5 more.

(x-700) (d+5) = xd

xd – 700d +5x – 3500=xd

5x – 700d – 3500=0

X-140d-700=0

But x=42000/d

42000/d – 140d – 700=0

42000 – 140 d² – 700d = 0

140d² + 700d-42000=0

d² + 5d – 300 = 0

d² + 20d – 15d – 300 =0

d(d+20) – 15(d+20)

(d+20) (d-15)=0

d=-20 or 15 ;     d can be only 15

Since x=42000/d = 42000/15 = 2800

So the no.of days he stayed is 15 and the amount he spent is Rs.2800

If he spent Rs.700 less means, the amount spent will be Rs.2100 and the no.of days he stayed will be 42000/2100 = 20 days which is 5 more days than 15.

Puzzle: 208                                                                                                                            10.07.2018

Ganesh went to Bangalore to enjoy for some days with an amount of Rs.42000. He started spending daily and after some days he found that all the money has been spent. While recalculating he finds that if he had spent Rs.700 less on each day, he could have stayed for five more days. How many days did he stay in Bangalore?

The answer for puzzle-207: 22 children

Solution for puzzle-207:

Between 7^th and 18^th there will be the 10 children excluding 7^th and 18^th

Similarly there will be 10 children in the opposite side.

So total = 10+ 10+2 (7^th + 18^th) = 22

Puzzle: 207                                                                                                                            09.07.2018

A number of children are standing in a circle. They are evenly spaced and the 7^th child is directly opposite to the 18^th child. How many children are there?

The answer for puzzle-206: The value of alphabets are N= 2 ; O = 4 ; S = 1 or 5 ; M = 5 or 1 ; J=9 ; U=3 ; E=6

Solution for puzzle-206:

By having a look into the numbers, we can decide that N should be 1,2 or 3, since E cannot be more than 9. If we put N as 1 E will be 3.

We can put O as 7 to get 1 in the place of N in JUNE.

The U will become 3 which cannot be because E is already 3.

If we try N for 3, E will become 9.

We can put O as 1 to get the value of N in JUNE as 3.

Then the value of U also will be 3 which is also not correct.

If we put N=2, E will be 6

To get 2 for N in the value of JUNE, we have to put O as 4.

Then U will become 3.

In the first column N=2. Now the remaining letters are S,M and J.

Now 1 + 2 + S+M =J (1 is already from the addition for second column)

Now we can fix the values of S & M as 1 & 5 and J as 6. So the solution is

2442 + 5442 + 1442=9326

The value of alphabets are N= 2 ; O = 4 ; S = 1 or 5 ; M = 5 or 1 ; J=9 ; U=3 ; E=6