M l aggarwal understanding icse mathematics class 9 Solutions for Chapter 6 problems on simultaneous linear equations

The sum of the two numbers is 50 and their difference is 16. Find the numbers.

The sum of the two numbers is 50 and their difference is 16. Find the numbers.

A 700 gm dry fruit pack costs Rs. 216. It contains some almonds and the rest cashew kernel. If

almonds cost Rs. 288 ‘per kg and cashew kernel cost Rs. 336 per kg, what are the quantities of the

two dry fruits separately?

Drawing pencils cost 80 paise each and colored pencils cost Rs. 1.10 each. If altogether two

dozens of pencils cost Rs. 21.60, how many colored pencils are there?

The sum of two numbers is 2. If their difference is 20, find the numbers.

Shikha works in a factory. In one week, she earned Rs. 390 for working 47 hours, of which 7

hours were overtime. The next week she earned Rs. 416 for working 50 hours, of which 8 hours

were overtime. What is Shikha’s hourly earning rate?

The sum of the two numbers is 43. If the larger is doubled and the smaller is tripled, the difference

is 36. Find the two numbers.

The cost of 5 kg of sugar and 7 kg of rice is Rs. 153, and the cost of 7 kg of sugar and 5 kg of rice

is Rs. 147. Find the cost of 6 kg of sugar and 10 kg of rice.

The sum of the digits of a two-digit number is 7. If the digits are reversed, the new number

increased by 3 equals 4 times the original number. Find the number.

The class IX students of a certain public school wanted to give a farewell party to the outgoing

students of class X. They decided to purchase two kinds of sweets, one costing Rs. 70 per kg and

the other costing Rs. 84 per kg. They estimated that 36 kg of sweets were needed. If the total

the money spent on sweets was Rs. 2800, find how much sweets of each kind they purchased.

Three years hence a man’s age will be three times his son’s age and 7 years ago he was seven

times as old as his son. How old are they now?

Rectangles are drawn on line segments of fixed lengths. When the breadths are 6 m and 5 m

respectively the sum of the areas of the rectangles is 83 m². But if the breadths are 5 m and 4 m

respectively the sum of the areas is 68 m². Find the sum of the areas of the squares drawn on the

line segments.

If from twice the greater of two numbers 16 is subtracted, the result is half the other number. If

from half the greater number 1 is subtracted, the result is still half the other number. What are

the numbers.

Rectangles are drawn on line segments of fixed lengths. When the breadths are 6 m and 5 m

respectively the sum of the areas of the rectangles is 83 m². But if the breadths are 5 m and 4 m

respectively the sum of the areas is 68 m². Find the sum of the areas of the squares drawn on the

line segments.

There are 38 coins in a collection of 20 paise coins and 25 paise coins. If the total value of the

the collection is Rs. 8.50, how many of each are there?

The lengths (in metres) of the sides of a triangle are 2x + y/2, 5x/3 + y + ½ and 2x/3 + 2y + 5/2. If

the triangle is equilateral, find its perimeter.

A man has certain notes of denominations Rs. 20 and Rs. 5 which amount to Rs. 380. If the

a number of notes of each kind is interchanged, they amount to Rs. 60 less as before. Find the

a number of notes of each denomination.

On Diwali eve, two candles, one of which is 3 cm longer than the other are lighted. The longer

one is lighted at 530 p.m. and the shorter at 7 p.m. At 930 p.m. they both are of the same length.

The longer one burns out at 1130 p.m. and the shorter one at 11 p.m. How long was each candle

originally?

The ratio of two numbers is 2/3. If 2 is subtracted from the first and 8 from the second, the ratio

becomes the reciprocal of the original ratio. Find the numbers.

If 1 is added to the numerator of a fraction, it becomes 1/5; if 1 is taken from the denominator,

it becomes 1/7, find the fraction.

If the numerator of a certain fraction is increased by 2 and the denominator by 1, the fraction

becomes equal to 5/8 and if the numerator and denominator are each diminished by 1, the fraction

becomes equal to ½, find the fraction.

Find the fraction which becomes ½ when the denominator is increased by 4 and is equal

to 1/8, when the numerator is diminished by 5.

In a two-digit number, the sum of the digits is 7. If the number with the order of the digits

reversed is 28 greater than twice the unit’s digit of the original number, find the number.

A number of two digits exceeds four times the sum of its digits by 6 and it is increased by 9 on

reversing the digits. Find the number.

When a two-digit number is divided by the sum of its digits the quotient is 8. If the ten’s digit is

diminished by three times the unit’s digit the remainder is 1. What is the number?

The result of dividing the number of two digits by the number with digits reversed is 1¾. If the sum of digits is 12, find the number.

The result of dividing a number of two digits by the number with the digits reversed is 5/6. If

the difference of digits is 1, find the number.

A number of three digits has a hundred digits 4 times the unit digit and the sum of three

digits are 14. If the three digits are written in the reverse order, the value of the number is

decreased by 594. Find the number.

Four years ago Marina was three times old as her daughter. Six years from now the mother

will be twice as old as her daughter. Find their present ages.

A person invested some money at 12% simple interest and some other amount at 10% simple

interest. He received a yearly interest of Rs, 1300. If he had interchanged the amounts, he would

have received Rs. 40 more as yearly interest. How much did he invest at different rates?

A shopkeeper sells a table at 8% profit and a chair at a 10% discount, thereby getting Rs. 1008.

If he had sold the table at 10% profit and the chair at an 8% discount, he would have got Rs. 20 more.

Find the cost price of the table and the list price of the chair.

A and B have some money with them. A said to B, “if you give me Rs. 100, my money will

become 75% of the money left with you.” B said to A” instead if you give me Rs. 100, your money

will become 40% of my money. How much money did A and B have originally?

The students of a class are made to stand in (complete) rows. If one student is extra in a row,

there would be 2 rows less, and if one student is less in a row, there would be 3 rows more. Find

the number of students in the class.

A jeweler has bars of 18-carat gold and 12- carat gold. How much of each must be melted

together to obtain a bar of 16-carat gold weighing 120 grams? (Pure gold is 24 carat)

A and B together can do a piece of work in 15 days. If A’s one day work is 1½ times the one

day’s work of B, find in how many days can each do the work.

2 men and 5 women can do a piece of work in 4 days, while one man and one woman can finish

it in 12 days. How long would it take for 1 man to do the work?

A train covered a certain distance at a uniform speed. If the train had been 30 km/hr faster, it

would have taken 2 hours less than the scheduled time. If the train were slower by 15 km/hr, it

would have taken 2 hours more than the scheduled time. Find the length of the journey.

A boat takes 2 hours to go 40 km down the stream and it returns in 4 hours. Find the speed of

the boat in still water and the speed of the stream.

A boat sails a distance of 44 km in 4 hours with the current. It takes 4 hours 48 minutes longer

to cover the same distance against the current. Find the speed of the boat in still water and the

speed of the current.

An airplane flies 1680 km with a headwind in 3.5 hours. On the return trip with same wind

blowing, the plane takes 3 hours. Find the plane’s airspeed and the wind speed.

A part of monthly hostel charges is fixed and the remaining depends on the number of days

one has taken food in the mess. When Bhawana takes food for 20 days, she has to pay Rs. 2600 as

hostel charges; whereas when Divya takes food for 26 days, she pays Rs. 3020 as hostel charges.

Find the fixed charges and the cost of food per day.