Q.1 The sum of two numbers is 60 and their difference is 14. Find the numbers.

__Answer:__

Let the two numbers be

Add (i) and (ii)

Therefore

Hence the two numbers are

Q.2 Twice a number is equal to thrice the other number. If the sum of the numbers is 85, find the numbers.

__Answer:__

Let the two numbers are

Solving for

or

Therefore

Hence the two numbers are .

Q.3 Find two numbers such that twice the first added to thrice the second gives 70 and twice the second added to thrice the first gives 75.

__Answer:__

Let the numbers be

Solving for

Multiply i) by 2 and ii) by 3 and subtract ii) from i)

Substituting in i)

Hence the two numbers are

Q.4 Find two numbers which differ by 9 and are such that four times the larger added to three times the smaller gives 92.

__Answer:__

Let the numbers be

Solving by

Multiply i) by 4 and subtract ii) from i)

Calculating for

Hence the two numbers are

Q.5 The sum of two numbers is 30 and the difference of their squares is 180. Find the numbers.

__Answer:__

Let the two numbers be

Simplifying ii)

Solving for

Add i) and iii)

Substituting in i)

Hence the numbers are

Q.6 The sum of the digits of a two-digit number is 8. On adding 18 to the number, its digits are reversed. Find the number.

__Answer:__

Let the two digit numbers be

Simplifying ii)

Solving for

Add i) and iii)

Substituting in i)

Hence the numbers is

Q.7 Two digit number is three times the sum of its digits. lf 45 is added to the number, its digits are reversed. Find the original number.

__Answer:__

Let the two digit numbers be

Simplifying i) and ii)

Solving for

Multiplying iv) by 7 and Subtract iv) from ii)

Hence

Therefore the numbers is

Q.8 A two-digit number is seven times the sum of its digits. lf 27 is subtracted from the number, its digits get interchanged. Find the number.

__Answer:__

Let the two digit number be

Solving for

Multiplying ii) by 3 and Subtract ii) from i)

Hence

Therefore the numbers is

Q.9 Find a fraction which reduces to 2/3 when 3 is added to both its numerator and denominator; and reduces to 3/5 when 1 is added to both its numerator and denominator.

__Answer:__

Let the fraction be

Solving for

Multiplying i) by 5 and ii) by 3 and subtract ii) from i)

Hence

Therefore the fraction is

Q.10 On adding 1 to the numerator of a fraction, it becomes ½. Also, on adding 1 to the denominator of the original fraction, it becomes 1/3. Find the original fraction.

__Answer:__

Let the fraction be

Solving for

Multiplying i) by 3 and ii) by 2 and subtract ii) from i)

Hence

Therefore the fraction is

Q.11 In a given fraction, if the numerator is multiplied by 2 and the denominator is reduced by 5, we get 6/5. But, if the numerator of the given fraction is increased by 8 and the denominator is doubled, we get 2/5. Find the fraction.

__Answer:__

Let the fraction be

Solving for

Multiplying ii) by 2 and subtract ii) from i

Hence

Therefore the fraction in

Q.12 5 years ago, a lady was thrice as old as her daughter. 10 years hence, the lady would be twice as old as her daughter. What are their present ages?

__Answer:__

Let the present age of lady

Let the Present age of Daughter

Solving for

Subtract ii) from i)

Hence

Therefore :

Lady’s Age

Daughter’s Age

Q.13 The sum of the ages of A and B is 39 years. In 15 years’ time, the age of A will be twice the age of B. Find their present ages.

__Answer:__

Let A’s Age

Let B’s Age

Solving for

Subtract ii) from i)

or

Therefore

A’s Age

B’s Age

Q.14 A is 15 years elder than B. 5 years ago A was four times as old as B. Find their present ages.

__Answer:__

Let the age of B

Hence A’s Age

Therefore

B’s Age

A’s Age

Q.15 Six years ago, the ages of Geeta and Seema were in the ratio 3 : 4. Nine years hence, their ages will be in the ratio 6 : 7. Find their present ages.

__Answer:__

Let the age of Geeta

Let the age of Seema

Solving for

Multiplying i) by 7 and ii) by 4 and Subtract ii) from i)

Hence

Therefore

Geeta’s Age

Seema’s Age

Q.16. 4 knives and 6 forks cost Rs. 200, while 6 knives and,7 forks together cost Rs. 264. Find the cost of a knife and that of a fork.

__Answer:__

Let the cost of knives

Let the Cost of fork

Solving for

Multiplying i) by 3 and ii) 2

Hence

Hence Cost of :

Knive

Fork

Q.17 The cost of 13 cups and 16 spoons is Rs. 296, while the cost of 16 cups and 13 spoons is Rs. 284. Find the cost of2 cups and 5 spoons.

__Answer:__

Let the cost of Cup

Let the Cost of Spoon

Solve for

Multiply i) by 16 and ii) by 13 and subtract ii) from i)

Hence

Hence Cost of:

Cup

Spoon

Q.18 Rahul covered a distance of 128 km in 5 hours, partly on bicycle at 16 kmph and partly on moped at 32 kmph. How much distance did he cover on moped?

__Answer:__

Total Distance

Total Time

Let the distance covered by cycle

Let the Distance covered by moped

Simplify

Hence Distance Covered by:

Cycle

Moped

Q.19 A boat can go 75 km downstream in 5 hours and, 44 km upstream in 4 hours. Find i) the speed of the boat in still water (ii) the rate of the current.

__Answer:__

Let the Speed of boat in still water

Speed of Stream

Solve for , add i) and ii)

Speed of Stream

Q.20 The monthly incomes of A and B are in the ratio 4 : 3 and their monthly savings are in the ratio 9 : 5. If each spends Rs. 3500 per month, find the monthly income of each.

__Answer:__

Let A’s Income

Let B’s Income

Substituting

Hence

Therefore :

A’s Income

B’s Income

Q.21 6 nuts and 5 bolts weigh 278 grams, while 8 nuts and 3 bolts weigh 268 grams. Find the weight of each nut and that of each bolt. How much do 3 nuts and 3 bolts weigh together?

__Answer:__

Let the Weight of Nut

Let the Height of Bolt

Solving for

Multiply i) by 8 and ii) by 6 and Subtract ii) from i)

Hence

Weight of:

Nut

Bolt

Therefore 3 Nuts and 3 Bolts will weight

Q.22 There are some girls in two classrooms, A and B. If 12 girls are sent from room A to room B, the number of girls in both the rooms will become equal. If 11 girls are sent from room B to room A, then the number of girls in room A would be double the number of girls in room B. How many girls are there in each class room?

__Answer:__

Let No. of girls in classroom

Solving ,

Subtract ii) from i)

Hence

No. of Girls in Class Room:

Q.23 4 men and 4 boys can do a piece of work in 3 days, while 2 men and 5 boys can finish it in 4 days. How long would it take 1 man alone to do it?

__Answer:__

Suppose 1 man finished the work in days and 1 Boy finished the work in days

There 1 man’s 1 day’s

And, 1 Boy’s 1 Day’s work

Now 4 men and 4 Boys finished the work in 3 days

Similarly 2 men and 5 boys finished in 4 days

Solving for

Multiply ii) by 2 and Subtract ii) from 2

or

Similarly

So one men can finished the work in

Q.24 A takes 3 hours longer than B to walk 30 km. But, if A doubles his pace, he is ahead of B by 1 hour 30 minutes. Find the speeds of A and B.

__Answer:__

Let the Speed of A

Let the Speed of B

Time taken By A

Time Taken By B

If A Double him Race Time taken by A

Therefore

Hence

Q.25 If the length of a rectangle is reduced by 1 m and breadth increased by 2 m, its area increases by 32 m^{2}. If however, the length is increased by 2 m and breadth reduced by 3 m, then the area is reduced by 49 m^{2}. Find the length and breadth of the rectangle.

__Answer:__

Let the Length of the rectangle

Let the Breadth of the rectangle

Solving for

From i)

Substituting in ii)

Hence

Therefore:

Length

Breadth

Sir, may I know the font you use.

Love that font 🙂

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Cambria Math

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