Aptitude and Reasoning Questions

There are total 5 ways.
we have only one kg of weight so,
2kg = 1kg + 1kg
4kg = 1 + 2 + 1
8kg = 1 + 2 + 4 + 1
16kg = 1 + 2 + 4 + 8 + 1
31kg = 1 + 2 + 4 + 8 + 16
So 5 weights are needed.

                      Article I                   Article II
                         -20                         25%
                                        5%
                         20%                       25%
                     

                          4              :              5

Now, Selling of first article = (4-20%) = 0.8

Selling of second article = (5+25%) =  6.25

Therefore the ratio of selling price = 8 : 62.5

Let the expenditure on the 95 students be 'x'

Then,

95x + 500 = 120(x – 5)
95x + 500 = 120x - 600
120x - 95x = 1100
25x = 1100
=> x = 44

Therefore, total expenditure of the hostel becomes
95 x 44 + 500 = 4680.

The transportation gets effect due to the flood created by incessant rains in the most rural parts of State. Therefore, on account of this, it is possible to increase the vegetable prices in the local market.

Let x, x+2, x+4, x+6, x+8 and x+10 are six consecutive odd numbers.

Given that their average is 52

Then, x + x+2 + x+4 + x+6 + x+8 + x+10 = 52×6

6x + 30 = 312

x = 47

So Product = 47 × 57 = 2679

Given 5:6 :: 7:10 :: 6:5

We know that compound ratio is calculated as
a:b :: c:d :: e:f
(axcxe):(bxdxf)

=> (5x7x6):(6x10x5)
=> (210):(300)
= 7:10

7 does not occur in 1000. So we have to count the number of times it appears between 1 and 999. Any number between 1 and 999 can be expressed in the form of xyz where 0 < x, y, z < 9.

1. The numbers in which 7 occurs only once. e.g 7, 17, 78, 217, 743 etc

This means that 7 is one of the digits and the remaining two digits will be any of the other 9 digits (i.e 0 to 9 with the exception of 7)

You have 1*9*9 = 81 such numbers. However, 7 could appear as the first or the second or the third digit. Therefore, there will be 3*81 = 243 numbers (1-digit, 2-digits and 3- digits) in which 7 will appear only once.

In each of these numbers, 7 is written once. Therefore, 243 times.

2. The numbers in which 7 will appear twice. e.g 772 or 377 or 747 or 77

In these numbers, one of the digits is not 7 and it can be any of the 9 digits ( 0 to 9 with the exception of 7).

There will be 9 such numbers. However, this digit which is not 7 can appear in the first or second or the third place. So there are 3 * 9 = 27 such numbers.

In each of these 27 numbers, the digit 7 is written twice. Therefore, 7 is written 54 times.

3. The number in which 7 appears thrice - 777 - 1 number. 7 is written thrice in it.

Therefore, the total number of times the digit 7 is written between 1 and 999 is

243 + 54 + 3 = 300