An employer finds that if he increases the weekly wages of each worker by ₹ 5 and employs five workers less, he increases his weekly wage bill from ₹ 3 , 150 to ₹ 3 , 250 . Taking the original weekly wage of each worker as ₹ x ; obtain an equation in x and then solve it to find the weekly wages of each worker.

Assume original weekly wage of each worker = Rs x According to question:- Original weekly wage bill of employer = Rs 3150 Number of workers = 3150 x New weekly wage of each worker = Rs ( x + 5 ) New weekly wage bill of employer = Rs 3250 Number of workers = 3250 x + 5 From the given condition, 3150 x - 5 = 3250 x + 5 3150 - 5 x x = 3250 x + 5 3150 x - 5 x 2 + 15750 - 25 x = 3250 x - 5 x 2 + 15750 - 125 x = 0 x 2 + 25 x - 3150 = 0 x 2 + 70 x - 45 x - 3150 = 0 x ( x + 70 ) - 45 ( x + 70 ) = 0 ( x + 70 ) ( x - 45 ) = 0 x - 70 = 0 OR x - 45 = 0 x = - 70 OR x = 45 So, wage cannot be negative, x = 45 . Hence, the original weekly wage of each worker is Rs 45 .

HARD

10th ICSE

IMPORTANT

Earn 100

One year ago, a man was $8$ times as old as his son. Now his age is equal to the square of his son's age. Find their present ages.

Important Questions on Solving (Simple) Problems (Based On Quadratic Equations)

HARD

10th ICSE

IMPORTANT

Concise Mathematics>Chapter 6 - Solving (Simple) Problems (Based On Quadratic Equations)>EXERCISE>Q 6

The age of a father is twice the square of the age of his son. Eight years hence, the age of the father will be

4

years more than three times the age of the son. Find their present ages.

HARD

10th ICSE

IMPORTANT

Concise Mathematics>Chapter 6 - Solving (Simple) Problems (Based On Quadratic Equations)>EXERCISE>Q 7

The speed of a boat in still water is

15 km / hr

. It can go

30 km

upstream and return downstream to the original point in

4

hours

30

minutes. Find the speed of the stream.

HARD

10th ICSE

IMPORTANT

Concise Mathematics>Chapter 6 - Solving (Simple) Problems (Based On Quadratic Equations)>EXERCISE>Q 8

Mr. Mehra sends his servant to the market to buy oranges worth

₹ 15

. The servant having eaten three oranges on the way, Mr. Mehra pays

25

paise per orange more than the market price. Taking

x

to be the number of oranges which Mr. Mehra receives, form a quadratic equation in

x

. Hence, find the value of

x

HARD

10th ICSE

IMPORTANT

Concise Mathematics>Chapter 6 - Solving (Simple) Problems (Based On Quadratic Equations)>EXERCISE>Q 9

₹ 250

is divided equally among a certain number of children. If there were

25

children more, each would have received

50

paise less. Find the number of children.

HARD

10th ICSE

IMPORTANT

Concise Mathematics>Chapter 6 - Solving (Simple) Problems (Based On Quadratic Equations)>EXERCISE>Q 10

An employer finds that if he increases the weekly wages of each worker by

₹ 5

and employs five workers less, he increases his weekly wage bill from

₹ 3, 150

₹ 3, 250

. Taking the original weekly wage of each worker as

₹ x

; obtain an equation in x and then solve it to find the weekly wages of each worker.

HARD

10th ICSE

IMPORTANT

Concise Mathematics>Chapter 6 - Solving (Simple) Problems (Based On Quadratic Equations)>EXERCISE>Q 11

A trader bought a number of articles for $₹ 1, 200$ . Ten were damaged and he sold each of the remaining articles at $₹ 2$ more than what he paid for it, thus getting a profit of $₹ 60$ on the whole transaction?

Taking the number of articles he bought as $x$ , form an equation in $x$ and solve it.

HARD

10th ICSE

IMPORTANT

Concise Mathematics>Chapter 6 - Solving (Simple) Problems (Based On Quadratic Equations)>EXERCISE>Q 12

The total cost price of a certain number of identical articles is

₹ 4, 800

. By selling the articles at

₹ 100

each, a profit equal to the cost price of

15

articles is made. Find the number of articles bought.

EASY

10th ICSE

IMPORTANT

Concise Mathematics>Chapter 6 - Solving (Simple) Problems (Based On Quadratic Equations)>EXERCISE>Q 1

The distance by road between two towns $A$ and $B$ is $216 km$ , and by rail it is $208 km$ . A car travels at a speed of $x km / hr$ and the train travels at a speed which is $16 km / hr$ faster than the car. Calculate the time taken by the car to reach town $B$ from $A$ , in terms of $x$ .

One year ago, a man was 8 times as old as his son. Now his age is equal to the square of his son's age. Find their present ages.

Important Questions on Solving (Simple) Problems (Based On Quadratic Equations)

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One year ago, a man was $8$ times as old as his son. Now his age is equal to the square of his son's age. Find their present ages.