Shortcuts for App

8/14/2019 Shortcuts for App

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Short Cut 1If the sum of two numbers is A and their difference is a, then the ratio of the numbers is given by:

A+a:A-aExample 1

The sum of two numbers is 36 and their difference is 6. What is the ratio of the numbers?

Solution 1

Here, A= 36 and a = 6,

Putting the value in equation:

A+a:A-aAnswer: 7:5

Short Cut 2:A number which when added to the terms of the ratio a:b makes it equal to the ratio c:d is:

Example 2:

Find the number which when added to the terms of the ratio 13:28 makes it equal to the ratio 1:2.

Solution 2

Here a: b= 13:28 and c:d= 1:2

Putting the values in the equation:

Answer= 2

Short Cut: Day 20

Short Cut 1If the sum of two numbers is A and their difference is a, then the ratio of the numbers is given by:

A+a:A-aExample 1


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The sum of two numbers is 36 and their difference is 6. What is the ratio of the numbers?

Solution 1

Here, A= 36 and a = 6,

Putting the value in equation:

A+a:A-aAnswer: 7:5

Short Cut 2:A number which when added to the terms of the ratio a:b makes it equal to the ratio c:d is:

Example 2:

Find the number which when added to the terms of the ratio 13:28 makes it equal to the ratio 1:2.

Solution 2

Here a: b= 13:28 and c:d= 1:2

Putting the values in the equation:

Answer= 2

Short Cut: Day 19

Short Cut 1The average of marks obtained by n candidates in a certain examination is T. If the average marks ofpassed candidates is P and that of failed candidates is F. Then the number of candidates who passedthe exam is given by:


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Example 1:The average marks obtained by 90 candidates in a certain examination is 38, if the average marks ofpassed candidates is 40 and that of the failed candidates is 30, what is the number of candidates who

passed the exam?Solution:Here: n= 90, T=38, F= 30 and P= 40, putting the values in the equation:

Answer= 72Short Cut 2The average of marks obtained by n candidates in a certain examination is T. If the average marks of

passed candidates is P and that of failed candidates is F. Then the number of candidates who passedthe exam is given by:

Example 2:The average marks obtained by 90 candidates in a certain examination is 38, if the average marks of

passed candidates is 40 and that of the failed candidates is 30, what is the number of candidates whofailed the exam?Solution:Here: n= 90, T=38, F= 30 and P= 40, putting the values in the equation:

Answer: 18

Short Cut for Math: Day 18

Short Cut 1:If a seller by selling N articles, gains or losses the cost price of n articles, then the gain or loss percentage

is calculated as:


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Find the number which when multiplied by 10 is increased by 261?

Solution

Here, x= 10 and y= 261. Putting the values in equation:

Answer: 29

Short Cut 2:In case of partnership, if investment of three partners are in ratio a:b:c and the timings are in ratio x:y:z then

the profit are in the ratio:

ax: by: cz

Example 2:A,B and C invested capitals in the ratio 5:6:8. The investment timing is in ratio 2:3:4. Find the ratio of the

profits?

Solution:

Here, a=5, b=6, c=8 and x=2, y=3, z=4. Putting the values in equation:

ax: by: cz

Answer: 10: 18: 32

Short Cut: Simple Interest

Short Cut 1:If a sum of money become x times in t years, at Simple Interest, then the rate of interest is given by:

Example 1:

A scheme in Muthoot Finance claim to double any amount in 5 years at simple interest. What is the rate of

effective rate of interest?

Solution 1:

Here, x=2 and t= 5 and putting the values in equation:


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Answer= 20%

Short Cut 2:A certain sum of money amounts to Rs A1 in t years at r% per annum, then the time in which it will amount

to Rs A2 at the same rate of interest is given by:

Example 2:

A certain sum of money amounts to Rs 4800 in 5 years at 4% per annum. In how many years it will amount

to Rs 5120 at the same rate.

Solution 2:

Here, A2= 5120, A1= 4800, t= 5 and r= 4

Putting the values in the equation

Answer: 7 years

Short Cut 3:If a sum of money becomes n times in t years at Simple Interest, then the time in which it will amount to

m times is given by:

Example 3:

If a sum of money doubles itself in 4 years at simple interest. How long will it take for the amount to be 10

times?

Solution 3:

Here, n= 2, t= 4 and m= 10

Putting values in equation:

Answer= 36 years.


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Streams: Short Cuts

Short Cut 1:If the speed of boat in still water is x km/hr and the speed of stream is y km/hr. If the boat travels for T

hours, then distance covered is given by:

Distance travelled upstream in time T is given by:

(x-y)*TDistance travelled downstream in Time T is given by:

(x+y)*TExample 1:If the speed of boat in still water is 10 km/hr and the speed of stream is 5 km/hr. If the boat travels for 3hours upstream and 2 hours downstream, what is the total distance covered?

Solution 1:Here, x= 10, y=5 and T= 2

Distance travelled upstream is:

(x-y)*TDistance travelled upstream is: 10 km

Distance travelled downstream is:

(x+y)*TDistance travelled upstream is: 30 km

Answer:Total distance travelled is: 40 km

Short Cut 2:A man can row x km/hr in still water. If in a stream which is flowing at y km/hr, it takes him T hrs to row to a

place and back. The distance between two places is given by:

Example 2:

A man can row 5km/hr in still water. If the river is running at 1.5 km/hr, it takes him 1 hour to row to a place

and back. How far is the place?

Solution 2:

Here x= 5, y= 1.5, T= 1

Putting the value:


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Answer= 2.275 km

Short Cut 3:A man rows a certain distance downstream x hours and returns the same distance in y hours. If the stream

flows at the rate of z km/hr then the speed of man in still water is given by:

Example 3:

Ram can row a certain distance downstream in 6 hours and return the same distance in 9 hours. If thestream flows at the rate of 3 km/hr find the speed of Ram in still water.

Solution 3:

x=6, y=9 and z=3

Answer: 15 km/hr

Short Cut: Day 14

Short Cut 1:To find the greatest number that will divide given numbers say x1, x2, x3.xn so as to leave the same remainder in each

case, we find the HCF of the positive difference of numbers i.e. HCF of:

Ix1-x2I, Ix2-x3I, Ix3-x4I and

Example 1:Find the greatest number which when divide 55, 127 and 175 leaves the same remainder in each case?

Solution 1:Here x1= 55, x2= 127 and x3= 175

The values of: Ix1-x2I, Ix2-x3I, Ix3-x1I are 72, 48, 120

HCF of 72, 48 and 120 is 24

Answer= 24

Short Cut 2:

To find the greatest number which will divide x , y and z leaving remainders a, b and c respectively is given by:

H.C.F of (x-a), (y-b) and (z-c).


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Example 2:What is the greatest number that will divide 29, 60 and 103 and will leave remainders 5, 12 and 7 respectively?

Solution 2:Here, x= 29, y= 60 and z=103

Also, a= 5, b=12 and c=7

Thus, (x-a), (y-b) and (z-c) are 24, 48 and 96. HCF of these numbers is 24.

Answer= 24

Short Cut 3:To find the least number which, when divided by x, y and z leaves the same remainder r in each case is given by :

L.C.M of (x,y,z) + r

Example 3:

Find the least number which when divided by 2, 3, 5 and 7 leaves the remainder 1.

Solution 3:

The least number is given by L.C.M of (2,3,5,7) + 1

Answer= 211

Short Cuts

Short Cut 1:If the value of a number is first increased by x% and later decreased by x% then the resultant value is always less than the

original value. The percent decrease is given by:

Example 1:

The salary of a worker is first increased by 10% and thereafter it was reduced by 10%. What was the net change in the salary?

Solution:

The net effect on the salary is decrease in following percentage:

Where x=10

Answer= 1% decrease

Short Cut 2:


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If first value is r% more then the second value, then the second value is lesser by first by following percentage:

Example 2:If the salary of Manish is 25% greater than Abhishek, than by how much percentage in the salary of Abhishek less then

Manish?

Solution 2:Here r= 25

Thus, putting the value we get:

Answer= 20%

Short Cut 3:If first value is r% less then the second value, then the second value is lesser by first by following percentage:

Example 3:

If the salary of Manish is 20% lesser than Summit, than by how much percentage in the salary of Abhishek less then Manish?

Solution: Putting r= 20

Answer= 25%

Short Cuts: Pipes and Cisterns

Short Cut: 1If a pipe fills the tank in x hours, and another fills the same tank in y hours and the third fills the tank in z hour. Then the time

required, if all the three pipes are open together to fill the tank is:

Example:Three pipes can fill the tank in 20, 30 and 40 hours respectively. Find the time required to fill the tank if all the pipes are filled

simultaneously.


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Solution

Here; x= 20, y= 30 and z= 40 hours

Putt ing the values in

We get answer= 17.14 hours

Short Cut: 2If pipe A can fill a tank in x minutes, pipe B can fill the same in y minutes, there is also an outlet C in the Tank. All the se are

opened simultaneously and the tank takes T minutes to get filled. The time in which C can empty the tank in minutes is given

by:

Example:Two pipes can fill a cis tern in 60 minutes and 75 minutes respectively. There is also an outlet C, if all the three pipes are

opened together, the tanks get filled in 50 minutes. Find the time taken by C to empty the full tank?

Answer:Here, x= 60, y= 75 and T= 50 minutes, put ting the values in equation:

Answer= 100 minutes

Short Cut 3A tap M can empty a tank in x minutes, while another tap N can empty it in y minutes. If both the emptying taps are opened

together, then the time taken to empty the full tank is:

ExampleA tap can empty the tank in 10 minutes; another tap can do the same in 5 minutes. Find the time required by both the taps to

empty the tank simultaneously?

SolutionHere x= 10 and y= 5, putting the values we get:

Answer= 3.33 minutes


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Number System: Short Cuts

Short Cut 1:If the sum of a number and its square is x, then the number is given by:

Example:

If the sum of a number and its square is 156, find the number

Solution:

Here x= 156

Putt ing the value in the formula:

Answer= 12

Short Cut 2:If the sum of two numbers is s and their difference is d. Then the product of the number is given by:

Example:The sum of two numbers is 38 and the difference is 4, find the product of the two numbers:

Solution:

Here s= 38 and d= 4, putting the values in the formula:

We get: Answer= 357

Short Cut 3

If the ratio of the sum and the difference of two number is a:b, then the ratio of these two numbers is given by:

Example 3:Ratio of the sum and the differences of the two numbers is 13:3, find the ratio of these two numbers

Solution:


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Here, a=13 and b=3

Putting the value:

Answer= 8:5

Short Cut related to Population

Short Cut 1If the present populat ion of a place is P, and it annually increases at the rate r%. The population at the end of n years is given

by:

Short Cut 2If the population of a place in the current year is P, it increases at a rate of x% for the first year, increases at the rate of y% for

the second year and z% for the third year. The population after third is given by:

Short Cut 3If the population of a place in the current year is P, it decreases at a rate of x% for the first year, increases at the rate of y% for

the second year and z% for the third year. The population after third is given by:

Short Cut 4If the population of a place in the current year is P, it increases at a rate of x% for the first year, decreases at the rate of y% for

the second year and again increases at z% for the third year. The population after third is given by:

To Square a Number Ending in 1Example : 41 x 41

Solution by steps:

(a) Square the next lower number (always ends with zero) 40 x 40 = 1,600

(b) Obtain the sum of the next lower number and the number being squared: 40 + 41 = 81

(c ) Add (a) and (b): 1,600 + 81 = 1,681, answer

Short way: 40 x 40 = 1,600; 40 + 41 = 81; answer 1,681


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To Square a Number Ending in 9Example : 39 x 39

Solution by steps :

(a) Square the next higher number 40 x 40 = 1,600

(b) Obtain the sum of the number being squared and the next higher number: 39 + 40 = 79

(c ) Subtract (a) and (b): 1,600 - 79 = 1,521, Answer

Short way: 40 x 40 = 1,600; -(39 + 40) = 1,521

To Square a number Ending in 5

Example : 35 x 35

Solution by steps :

(a) Multiply the first digit by the digit plus 1 : 3 x 4 = 12

(b) Attach 25 : 1,225,answer

Short way : 3 x 4 = 12;answer 1,225

Time and Work: Short Cuts

Short Cut 1:If A and B can do a piece of work in x days, B and C in y days and C and A in z days. Then A, B and C can together do the

work in:

Example 1:

If A and B can do a piece of work in 12 days, B and C in 15 days and C and A in 20 days. In how many days will, all of them

working together would take complete the work?

Solution:

Here x= 12, y= 15 and z= 20,

Putting values in formula:

Answer: 10 days

Short Cut 2:If A can do a work in x days, B can do the same work in y days. Together A and B can do the same work in:


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Example:2

If Ram can do a piece of work in 20 days, Shayam can do the same work in 30 days, in how many days Ram and Shayam will

together do the work?

Solution:

Here x= 20 and y= 30, putt ing values in formula we get:

Answer: 12 days

Short Cut 3:If A, B and C respectively can finish a work in x, y and z days, then all of them together would finish the work in following days:

Example 3:Amar, Akbar and Anthony can finish a work in 10, 15 and 20 days respectively. If they all work together, then in how many

days, they will be able to finish the work?

Solution:

Here x= 10, y=15 and z= 20

Putt ing the values in the formula:

We get:

Answer= 4.61 days

Profit and Loss: Short Cuts, Part-2

Short Cut 1:If the cost price of x articles is equal to the selling price of y articles, then the profit percentage is given by:


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Example 1:If Sudha sells 18 articles at the cost price of 24 articles. Find her profit percentage?

Solution:Here, x= 24 and y= 18

Putt ing the values in the formula

Answer= 33.3%

Short Cut 2:

A man purchases a certain number of articles at x a rupee and the same number at y a rupee. He mixes them together andsells them at z per rupee. Then his gain or loss percentage is given by:

Example 2:A man purchases a certain number of oranges at 7 per rupee and the same number at 15 per rupee. He mixes them together

and sells them at 12 per rupee. Determine his profit or loss percentage.

Solution:x= 7, y= 15 and z= 12, putting the values in the equation:

Answer: 20.45% at Loss

Short Cut 3:By selling an article for Rs A, a dealer makes a profit of x%. If he wants to make profit of y%, then he must increase his se lling

price by Rs:

The new selling price is given by:


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Profit and Loss: Short Cut

Short Cut 1If a shopkeeper wants to earn x% profit on an article after offering y% discount to the customer, to arrive at label price, the

marketed price should be increased by following percentage:

Example

If a dealer wants to earn 20% profit on an article after offering 50% discount to the customer, by what percentage should he

increase his marked price to arrive at a label price?

Solution:

Here, x=20%, y=50%

Putting the formula:

Answer= 140%

Short Cut-2If a seller uses X gm in place of 1000 gm to sell his goods and gains a profit of y% on cost price, then his actual gain or less

percentage is:

According as the sign is negative or positive.

Example:

A seller uses 840 gm in place of 1 kg to sell his goods. Find his actual % profit or loss, when he sells his article on 4% gain on

cost price.

Solution:

X = 840 gm, y=4

Putting values:

We get= 18.6%

Short Cut 3

A dishonest seller sells the goods at x% loss on the cost price but uses y% less weight to weigh the goods, than his percentage

profit or loss is:


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Here x= 4

So, Case 1:

= 24 minutes past 11

Case 2:

= 19.63 minutes past 11

Short Cut 3Between x and x+1 oclock the two hands are at right angle at :

Minutes Past x

Distance and Speed: Short Cut

Short Cut 1If a person travels half a distance in a journey at x km/hr and remaining half at the speed of y km/hr, the average speed of the

whole journey is given by:

Example 1

A person travels half of journey at the speed of 30 km/hr and the next half at a speed of 15 km/hr. What is the average speed of

the person during the whole journey?

Solution:

Here; x= 30 and y= 15

Putt ing the values we get:

Answer= 20 km/hr

Short Cut 2If a person travels three equal distances in a journey at a speed of x km/hr, y km/hr and z km/hr. The average speed is given

by:


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Example 2

Ravi starts from Delhi to Agra a distance of about 300 kms. He divided his journey into a distance of thee equal parts in terms

of distance and covered them with the speed of 30 km/hr, 60 km/hr and 90 km/hr, calculate his average speed during the

journey:

Solution:

Here: x= 30, y= 60, z= 90.


Answer= 49.09 km/hr

Short Cut 3If a person travels Mth part of a distance at x km/hr, Nth part at y km/hr and the remaining Pth part at z km/hr, then his average

speed in km/hr is given by:

If instead of proportion, the parts of the distance are given in percentage i.e. M%, N% and P% respectively, then the formula

becomes:

Example 3Hari travels 20% of a distance at an average speed of 20 km/hr, next 30% distance at an average speed of 30 km/hr and the

remaining 50% of distance at the average speed of 50 km/hr. Find his average speed during the whole journey.

Solution:

Here M=20, N=30 and P= 50 also x= 20, y= 30 and z= 50



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Answer = 33.33 km/hr

Averages: Short Cuts

Short Cut 1:

If the average age/weight/height etc of n objects is x and the average of m objects is y then the average of all of them put

together in a single group is:

Exam ple 1:The average age of 20 girls in a college is 21 years while the average age of 25 boys of the same same college is 22 years.

Find the combine average of the group.

Solution:

Applying the formula:

n= 20, m= 25, x= 21 and y = 22

Answer = 21.56

Short Cut 2:In a group if the average age/weight/height etc of n objects is x, and the average age/weight/height etc of m objects out

them in the group is y, then the average age/weight/height etc of remaining n-m objects is::

Example 2:

A group of 20 girls has average age of 12 years. Average age of first 12 from the same group is 13 years. What is the average

age of remaining 8 girls in the group.

Solution:

Applying the formula:


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If a number is increase successively by a% and b% the net effect on the original number is :

Case 2:If a number is decrease successively by a% and b% the net effect on the original number is:

The negative sign indicates net decrease in the orignal amount or number

Case 3:If a number is first decrease by a% and then increase by b% the net effect on the original number is:

The sign of result in such case would indicate that if the original number was increased or decreased.

Example 1:The tax on a commodity was reduced by 20% as a result its consumption increase by 15%. F ind the net effect on the revenue.

Solution:

It is the case of decrease in percentage followed by an increase.

Applying the formula here x= -20, y= 15

Thus net change in the orignal revenue is:

Answer: Decrease by 8%

Example 2:Peter England a well know brand of Clothes offer 30% and 70% discounts successively on Christmas on Men Shirt. What is the

actual discount offered by Peter England?


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Solution:

The formula for successive discount comes under the category of succesive decrease. The following in the formula

Where a= 30, b= 70;

Thus the net discount in this case is 79%.

Short Cut: Consumption and Cost

In a number of questions the increase or decrease in Consumption or cost is given in percentage and its effect on decrease or

increase in Cost or Consumption is asked in percentage. The two cases are as:

Case 1 : Increase in Cost leading to decrease in Consumption

If the price of a commodity is increased by x%, then reduction in consumption so as not to increase the expenditure is:

Example:

The price of cooking oil has increased by 25%. The percentage change of reduction that a family should effect in the use of

cooking oil so as not to increase the expenditure is :

Solution:

Applying the formula, here x% = 25%

So,

Case 2 : Decrease in Cost leading to increase in Consumption


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If the price of a commodity is decreased by x%, then increase in consumption so as not to increase the expenditure is:

Example:

The price of cooking oil has decreased by 25%. The percentage change of increase in consumption so that a family should

effect in the use of cooking oil so as not to decrease the expenditure is:

Solution:

Applying the formula, here x% = 25%

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