- If A had invested his sum at Simple Interest for 3 yr at the rate of R% p.a. instead in scheme S1 and B has invested his sum at compound Interest at (R + 5%) p.a. for 1 year and difference in interest obtained is 30,000 then find value of R%.
=>2400R – 300R – 1500 = 30000
=>8R – R – 5 = 100
=>7R = 105A
=>R = 15%
- Several litre of Acid were drawn off a 54-litre vessel full of Acid and an equal amount of water added. Again the same volume of the mixture was drawn off and replaced by water as a result the vessel contained 24 litres of pure acid. How much of the Acid was drawn off initially ?
30 litres25 litres10 litres22 litres18 litresOption E
Let initially x litres of Acid were drawn off 24=54(1−x/54)^2
=> 24 × 54 = (54 – x)^²
=> x² – 108x + 1620 = 0
=> x² – 90x – 18x + 1620 = 0
=> (x – 90) (x – 18) = 0
x = 18 litres
- Leela borrowed some money at the rate of 6% p.a. for the first three years, 9% p.a. for the next five years and 13% p.a. for the period beyond eight years. If the total interest paid by her at the end of eleven years is Rs. 8160, how much money did she borrow?
Rs. 6000Rs. 8000Rs. 7500Rs. 10000Rs. 9000Option B
Let the sum = x
Sum = Rs. 8000
- My brother is 3 years elder to me. My father was 28 years of age when my sister was born while my mother was 26 years of age when I was born. If my sister was 4 years of age when my brother was born, then, what was the age of my father and mother respectively when my brother was born?
25 years15years10 years23 years15 yearsOption D
Father’s age when brother was born = 28 + 4
= 32 years
Mother’s age when brother was born = 26 – 3
= 23 years
- A and B started a business together with an investment of Rs.3200 and Rs.4000 resp. After 3 months, C joined them with an investment equal to average initial investment of A and B taken together, and A withdrew 25% of his investment. After completion of a year they received a total profit of Rs. 18600. Find the profit share of C.
Investment of C = (3200+4000)/2 = Rs.3600
Ratio of investment of A, B and C = 3200:4000:3600
Ratio of profit share = (8*3+6*9): (10*12) : (9*9)
Profit share of A = 26/[26+40+27]*18600 = Rs.5400
- There was a leopard and a tiger walking in the two different rings of same radii in a circus,. A girl observed that when leopard moved three steps, tiger moved 5 steps in the same time, but the distance traversed by leopard in 5 steps is equal to the distance traversed by tiger in 4 steps. What is the number of rounds that a leopard made when tiger completed 100 rounds?
Ratio of speeds = Ratio of distances, when time is constant
Ratio of distance covered by Leopard to the tiger = 12 : 25
Again, Ratio of rounds made by Leopard to the tiger = 12 : 25
= 48 : 100
Hence, Leopard makes 48 rounds.
- B is thrice as efficient as A and A can do a piece of work in 21 days. A started working and after a few days B joined him. They completed the work in 15 days from the beginning. For how many days did they work together?
7 days6 days2 days4days8 daysOption C
A ——- B
Number of days = 21 —— 7(B is thrice as efficient as A)
One day’s work = 1/21 —– 1/7
A and B’s one day’s work = 1/21+1/7 = 4/21
Let B joined A after (15-x)days
=> 15 – x + 4x = 21
=> x = 2 days
- A tank is in the shape of a cuboid whose length is 8.4 m and breadth is 3.5 m water flows into it through a pipe at the rate of 14 metres per second. The cross-section of the pipe is 7 cm × 5 cm. Find the height up to which water level will rise in the tank in 60 minutes.
8 meter6 meter11 meter18 meter14meterOption B
Perimeter of the cuboid = l*b*h = 8.4*3.5*h
=> h = [7*5*14*60*60]/[8.4*3.5*100*100] => h = 6 meter
- Rajesh has a total of Rs.42,000. And in that, he lends Rs.8,000 at 9/2% per annum simple interest and Rs.12,000 at 8% per annum simple interest. He lends the remaining money at a certain rate of interest so that he gets total interest of Rs. 3600 at the end of one year. The rate of interest per annum, at which the remaining money is lent, is?
For first loan 𝑆𝐼=𝑃𝑁𝑅/100
For Second loan=12000×8×1/100
Total interest = 3600
So, for the third loan SI = 3600-(960+360) = 2280
Rate of interest for third loan=[2280×100]/22000
- If 6 years are subtracted from the present age of Ajay and the remainder is divided by 18, then the present age of Rahul is obtained. If Rahul is 2 years younger to Denis whose age is 5 years, then what is Ajay’s present age?
Present age of Denis = 5 years
Present age of Rahul =5−2=3
Let present age of Ajay = x
Then, present age of Rahul =x−6/18 [x−6]/18 = 3
=>x−6=3×18 = 54
=>x=54+6 = 60