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Published on: 09/10/2019
Algebra
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1.
A group of x boys planned to go on a summer vacation camp. Each bought food to last for 21 days. But due to some reason, 2x boys joined the camp later. Then, how many days would the same amount of food last?
2.
Karan scored 2 x marks in English and x marks in Mathematics. His score in Science was 60.If his total score for the three subjects was 180 then calculate his score in English.
3.
Three boxes weight are (k+ 4) kg, 2k kg and (3k - 4) kg. If the second box weight is 6 kg, find the total weight of the three boxes.
4.
In a village, there are 9 water tanks to collect rain water. On a particular day, x L of rain water is collected per tank. If 200 L of water was already there in one of the tanks, what is the total amount of water in the tanks on that day?
5.
Cost of 3 dozen bananas is Rs 54. Rehman has Rs 18 with him. He wants to give bananas to the poor people on the street.
(a) How many bananas he can buy?
(b) Mention the value depict from Rehman?
6.
Translate each of the following statements into an equation, using x as the variable.
(a) 13 subtracted from twice a number gives 3.
(b) One-fifth of a number is 5 less than that number.
(c) Two-third of a number is 12.
(d) 9 added to twice a number gives 13.
(e) 1 subtracted from one-third of a number gives 1.
7.
Form an equation for the given statements.
(a) When 14 is added to a number, the result is 70.
(b) The difference of a number with 3 is 10.
(c) Five times a number is 25.
(d) A number divided by 3 gives 15.
(e) Three is added to two times of a number given 13.
8.
Sonal got 5 marks less than that of Ritu in a competition. If Ritu got 15 marks, how many marks obtained by Sonal?
9.
Rahul scores 20 more runs than twice of the runs scored by Vipin. If Vipin made 10 runs, what is the score of Rahul?
10.
The perimeter of an equilateral triangle having each side x cm long is 15 cm. Find the length of the side.
1.
7 days
2.
80
3.
18 kg
4.
According to the question,
Tanks to collect rain water = 9
Rain water is collected per tank (in L) = x
Then, total rain water in tanks (in L)
= Number of tanks x Per tank collected rain water
= 9\(\times\)x = 9x
But in the one tank, already 200 L of water exist, then total amount of water is given by = 200 + [Total rain water in L]
= 200 + 9x or (9x + 200)L
5.
Let the cost of 1 dozen be Rs x.
Then, cost of 3 dozen = Rs 3x
According to the question,
\(3x=54 \Rightarrow x=\frac{54}{3}=18\)
∴ The cost of one dozen = Rs 18
Hence, Rehman can buy 1 dozen of bananas.
(b) Humanity, Helpfulness, caring for others.
6.
a) Let number be x.
Twice the number = 2x Then,2x-13=3
(b) Let the number be x.
One-fifth of this number =\(\frac{x}{5}\)
Then,\(\frac{x}{5}\)=x-5
(c) Let the number be x.
Two-third of this number =\(\frac{2}{3}x\)
∴ \(\frac{2x}{3}=12\)
(d) Let the number be x.
Twice of this number = 2x
Then, 2x + 9 =13
(e) Let the number be x.
One-third of this number =\(\frac{x}{3}\)
Then, \(\frac{x}{3}\)-1=1
7.
(a) Let the number be x.
Then, the required equation is x + 14 = 70
(b) Let the number be x.
Then, the required equation is x - 3 = 10
(c) Let the number be x.
Given, five times of x = 5x
∴ Required equation is 5x = 25
(d) Let the number be x.
One-third of x = \(\frac{x}{3}\)
Then, the equation is \(\frac{x}{3}\)=15
(e) Let the number be x.
Two times of this number = 2x
∴ The equation is 2x + 3 = 13
8.
10 marks
9.
40 runs
10.
5 cm
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