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DIRECTIONS : What will come in place of the question mark (?) in the following questions?
45% of 6400 - ? % of 4800 = 17 × 29 – 157
2880 - ? × 48 = 336
? × 48 = 2880 – 336 = 2544
? = 53
DIRECTIONS: Find the missing term in the following series.
46, 57, 81, 120, ?, 251
46 + 11 × 1 = 46 + 11 = 57
57 + 12 × 2 = 57 + 24 = 81
81 + 13 × 3 = 81 + 39 = 120
120 + 14 × 4 = 120 + 56 = 176
176 + 15 × 5 = 176 + 75 = 251
A vessel contains 16 litres solution of wine having 60% alcohol. How many litres of water is to be added to this solution, so that alcohol becomes 40% in the resultant solution?
In 16 litres of solution, quantity of alcohol = 60% of 16 = 9.6 litres
Now this 9.6 litres = 40% of resultant solution
Therefore, resultant solution = 9.6/0.4 litres = 24 litres
So, water added = 24 – 16 = 8 litres
Area of a square P is 1024 m2. Side of square Q is 4 m more than the side of the square P. What is 60% of the difference between their perimeters?
Area of square P = 1024 m2
Side of square P = = 32 m
Side of square Q = 32 + 4 = 36 m
Difference between their perimeters = 4(36 – 32) = 16 m
Required % = 60 % of 16 m = 9.6 m
The average age of all the seven children in a family is 10 years. If the age of the eldest person of the family is included, then the average age becomes 19 years. What is the age of the eldest person?
Let the age of the eldest person of the family be ‘x'. As the average age of seven children is 10 years and all the eight together is 19 years.
⟹ 7 (10) + x = 8 × 19
⟹ 70 + x = 152
⟹ x = 152 – 70 = 82.
Five years ago, the ages of Bali and Geeta were in the ratio of 3 : 4. Ten years hence the respective ratio of their ages will be 6 : 7. What is the difference between their present ages?
Let the ages 5 years ago were 3x and 4x.
Ages 10 years hence will be (3x + 15) and (4x + 15)
Therefore, (3x + 15)/(4x + 15) = 6/7
7(3x + 15) = 6(4x + 15)
21x + 105 = 24x + 90
3x = 15
x = 5
The difference between their ages = 4x – 3x = x = 5 years.
Three sides of a triangular field are 7 meters, 25 meters and 24 meters. If it is to be excavated and leveled at the rate of Rs. 130 per square meter, then what is the total cost of the work?
Given dimensions fulfill the condition of pythagoras theorem-
Thus,
7^2+24^2= 25^2
so
h=25
B=7
Area= 1/2 *7*24= 84 m^2
excavated and leveled at the rate = Rs. 130 per square meter
thus
Total Cost = 84×130 = 10920 Rs.
Alternate solution-
Area of triangle calculated by Heron's formula.
a=7 m
b=25 m
c= 24m
S= a+b+c/2
= (7+25+24)/2
= 56/2= 28
A bowl contains 4 red balls, 3 blue balls and 5 yellow balls. If three balls are drawn at random, the probability that the balls drawn are of different colors is?
A boat travelled 40 km downstream and 20 km upstream in 6 hours. The boat travelled another 56 km downstream and 34 km upstream in 9 hours. What is the speed of the water?
Let the speed of downstream = SD kmph
and speed of upstream = SU kmph
Then, (40/SD) + (20/SU) = 6---------(1)
(56/SD) + (34/SU) = 9--------(2)
By, 5 x eq(2) – 7 x eq(1)
30/SU= 3
SU= 10 kmph
now from eq (1), (40/SD) + 2 = 6
SD = 10 kmph
speed of water = (SD– SU)/2 = (10 – 10)/2 = 0 kmph
A and B invested Rs.40,000 and Rs.50,000 respectively in a business. B left the business with his money after 4 months and after 2 more months he rejoins the business with a capital of Rs.60,000. At the end of the first year they earned a profit of Rs. 1,560. What is the share of A in the profit?
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