- Percentage Change = (Final Value – Initial Value)/Initial Value * 100
- x % of T = $$\dfrac{x}{100}\times\ T$$
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Four unique even numbers are arranged in ascending order and the first two are decreased by 50%, while the last two are increased by 50%. If the original sum of the 4 numbers was 162, the new sum can be?
Let the numbers be 2a, 2b, 2c, 2d.
and $$a\le\ b\le\ c\le\ d$$
and at first, 2a + 2b + 2c + 2d = 162
which means a + b + c + d =81 --------equation (1)
and we have to find the value of a + b + 3c + 3d
which is (a + b + c + d) + 2c + 2d ; putting values from equation (1)
= 81 + 2c +2d
= 81 + 2 ( c + d ) ---------equation(2)
also if$$a\le\ b\le\ c\le\ d$$
$$then\ a+1\ \le\ \ b$$
$$\ b+1\ \le\ \ c$$
$$\ c+1\ \le\ \ d$$
from these equations :
$$\ a+2\ \le\ \ c$$ ---------------equation(3)
$$\ b+2\ \le\ \ d$$ ----------------equation(4)
adding equation (3) and (4)
$$a+\ b\le\ c+\ d-4$$ ----------- equation(5)
putting values of a+b from equation (5) to equation (1)
$$\ c+\ d-4\ +c\ +d\ \ge\ 81$$
$$2\left(c+d\right)\ge\ 85$$
$$c+d\ge\ 42.5$$
as c and d are natural numbers so $$c+d\ge\ 43$$
putting this value in equation (2)
a+b+3c+3d $$\ge\ $$ 81 + 2*(43)
a+b+3c+3d $$\ge\ $$ 167
which means the minimum value of the required equation is 167.
We only have one option greater than 167 which is 173.
Hence 173 is the answer.
Ajay bought two scooters at the same price. He sold one at a profit of 10% and the other at a loss of 10%. If he made a total of Rs. 30000 from the sales, what was the cost price of each scooter?
Let's assume the cost price of each scotter is x. The selling price of the scotter will be 0.9x, and that of the other one will be 1.1x
0.9X +1.1X = 30000.
So, X = Rs. 15000
Ram’s salary increased by 10%, 12%, and 15% in the first, second, and third years, respectively. Determine the average annual percentage increase in Ram’s salary (rounded to one decimal place)
Let the initial salary of Ram be ₹1.
Salary of Ram after increment = $$₹\left(1+10\%\right)\left(1+12\%\right)\left(1+15\%\right)=₹1.4168$$.
So, the salary of Ram increased by 41.68%.
Average yearly increment in his salary = $$\dfrac{41.68\%}{3}=13.89\%$$
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