Question / āĻĒā§ā§°āĻļā§āĻ¨: Find the amount obtained in 2 years on âš6,800 at 15% per annum compound interest, compounded annually (âš6,800 āĻāĻāĻžā§° āĻāĻĒā§°āĻ¤ 15% āĻŦāĻžā§°ā§āĻˇāĻŋāĻ āĻāĻā§āĻ°āĻŦā§āĻĻā§āĻ§āĻŋ āĻ¸ā§āĻĻā§° āĻšāĻžā§°āĻ¤ 2 āĻŦāĻā§°ā§° āĻĒāĻŋāĻāĻ¤ āĻŽāĻŋāĻļā§ā§°āĻ§āĻ¨ (Amount) āĻ¨āĻŋā§°ā§āĻŖāĻ¯āĻŧ āĻā§°āĻāĨ¤)
A. âš9,393 B. âš8,641 C. âš8,993 D. âš7,996
Formula / āĻ¸ā§āĻ¤ā§ā§° : A = P(1 + R/100â)n
Where / āĻ¯'āĻ¤
- P = âš6800 Principal / āĻŽā§āĻ˛āĻ§āĻ¨)
- R = 15% (Rate / āĻ¸ā§āĻĻā§° āĻšāĻžā§°)
- n = 2 years (āĻŦāĻā§°)
A = P(1 + R/100â)n
A = 6800(1+15/100)2 = 6800(1.15)2 = 6800 × 1.3225 = 8993
Therefore, the amount after 2 years is: âš8,993
==================================================================
Question / āĻĒā§ā§°āĻļā§āĻ¨: An article was purchased for âš8,900. Its price was marked 40% above the cost price. It was then sold at a 5% discount on the marked price. What was the profit percentage ? (āĻāĻāĻž āĻŦāĻ¸ā§āĻ¤ā§ âš8,900 āĻ¤ āĻā§ā§°āĻ¯āĻŧ āĻā§°āĻž āĻšā§āĻāĻŋāĻ˛āĨ¤ āĻāĻ¯āĻŧāĻžā§° āĻŽā§āĻ˛ā§āĻ¯ āĻā§ā§°āĻ¯āĻŧāĻŽā§āĻ˛ā§āĻ¯āĻ¤āĻā§ 40% āĻŦā§āĻāĻŋ āĻā§°āĻŋ āĻāĻŋāĻšā§āĻ¨āĻŋāĻ¤ (Marked Price) āĻā§°āĻž āĻš'āĻ˛āĨ¤ āĻ¤āĻžā§° āĻĒāĻŋāĻāĻ¤ āĻāĻŋāĻšā§āĻ¨āĻŋāĻ¤ āĻŽā§āĻ˛ā§āĻ¯ā§° āĻāĻĒā§°āĻ¤ 5% ā§°ā§āĻšāĻžāĻ āĻĻāĻŋ āĻŦāĻŋāĻā§ā§°ā§ āĻā§°āĻž āĻš'āĻ˛āĨ¤ āĻ˛āĻžāĻā§° āĻļāĻ¤āĻā§°āĻž āĻāĻŋāĻŽāĻžāĻ¨ ?)
A. 33% B. 32% C. 34% D. 35%
Shortcut / āĻāĻŽā§ āĻĒāĻĻā§āĻ§āĻ¤āĻŋ
Marked Price (MP) = 140% of CP
Selling Price (SP) = 95% of MP = 140% × 95% = 140 × 95/100 = 133%
Thus, SP = 133% of CP
Profit % = 133% − 100% = 33%
Ans / āĻāĻ¤ā§āĻ¤ā§° : A. 33%
Short Tricks
CP = âš8900
MP = 8900 ×1.40 = âš12460
SP = 12460 × 0.95 = âš11837
Profit = 11837 − 8900 = âš2937
Profit % = 2937 / 8900 × 100 = 33%
Ans: A. 33%
==================================================================================
Question / āĻĒā§ā§°āĻļā§āĻ¨: A and B together can complete a work in 6 days. B alone can complete the same work in 12 days. How many days will A alone take to complete twice the work ? (A āĻā§°ā§ B āĻ āĻāĻā§āĻ˛āĻā§ āĻāĻāĻž āĻāĻžāĻŽ 6 āĻĻāĻŋāĻ¨āĻ¤ āĻ¸āĻŽā§āĻĒā§ā§°ā§āĻŖ āĻā§°āĻŋāĻŦ āĻĒāĻžā§°ā§āĨ¤ B āĻ āĻ
āĻāĻ˛ā§ āĻāĻā§āĻāĻž āĻāĻžāĻŽ 12 āĻĻāĻŋāĻ¨āĻ¤ āĻ¸āĻŽā§āĻĒā§ā§°ā§āĻŖ āĻā§°āĻŋāĻŦ āĻĒāĻžā§°ā§āĨ¤ A āĻ āĻ
āĻāĻ˛ā§ āĻ¸ā§āĻ āĻāĻžāĻŽā§° āĻĻā§āĻā§āĻŖ āĻāĻžāĻŽ āĻ¸āĻŽā§āĻĒā§ā§°ā§āĻŖ āĻā§°āĻŋāĻŦāĻ˛ā§ āĻāĻŋāĻŽāĻžāĻ¨ āĻĻāĻŋāĻ¨ āĻ˛'āĻŦ ?)
A. 27 B. 12 C. 24 D. 25
Shortcut Trick / āĻāĻŽā§ āĻā§āĻļāĻ˛
A + B = 6 days , A+B=6 days, B=12 days
A = 6 × 12 / 12 − 6 = 72/6 = 12 days
So, A alone completes 1 work in 12 days. āĻ
ā§°ā§āĻĨāĻžā§, A āĻ āĻ
āĻāĻ˛ā§ ā§§āĻāĻž āĻāĻžāĻŽ 12 āĻĻāĻŋāĻ¨āĻ¤ āĻ¸āĻŽā§āĻĒā§ā§°ā§āĻŖ āĻā§°ā§āĨ¤
For double work / āĻĻā§āĻā§āĻŖ āĻāĻžāĻŽā§° āĻŦāĻžāĻŦā§: 12 × 2 = 24 days
Ans / āĻāĻ¤ā§āĻ¤ā§°: C. 24 days (24 āĻĻāĻŋāĻ¨)
Trick / āĻā§āĻļāĻ˛
If: (A+B) = x days, B = y days (āĻ¯āĻĻāĻŋ (A+B) = x āĻĻāĻŋāĻ¨ āĻā§°ā§ B = y āĻĻāĻŋāĻ¨ āĻšāĻ¯āĻŧ, āĻ¤ā§āĻ¨ā§āĻ¤ā§)
Then: A = xy / y − x ââ
āĻ¤āĻžā§° āĻĒāĻŋāĻāĻ¤ āĻĻā§āĻā§āĻŖ āĻāĻžāĻŽ āĻš'āĻ˛ā§ āĻāĻ¤ā§āĻ¤ā§°āĻ 2 ā§°ā§ āĻā§āĻŖ āĻā§°āĻŋāĻŦāĨ¤
=================================================================
Question / āĻĒā§ā§°āĻļā§āĻ¨: A vessel is filled 2/5â with blue liquid. One-third of the remaining part is filled with black liquid. Then 5/6â of the remaining part is filled with yellow liquid. The remaining 4.2 litres is white liquid. Find the total capacity of the vessel. (āĻāĻāĻž āĻĒāĻžāĻ¤ā§ā§°ā§° 2/5 āĻ
āĻāĻļ āĻ¨ā§āĻ˛āĻž āĻĻā§ā§°ā§ąā§°ā§ āĻā§°āĻžāĨ¤ āĻŦāĻžāĻā§ āĻ
āĻāĻļā§° 1/3 āĻ
āĻāĻļ āĻ'āĻ˛āĻž āĻĻā§ā§°ā§ąā§°ā§ āĻā§°āĻž āĻšāĻ¯āĻŧāĨ¤ āĻ¤āĻžā§° āĻĒāĻŋāĻāĻ¤ āĻŦāĻžāĻā§ āĻ
āĻāĻļā§° 5/6 āĻ
āĻāĻļ āĻšāĻžāĻ˛āĻ§ā§āĻ¯āĻŧāĻž āĻĻā§ā§°ā§ąā§°ā§ āĻā§°āĻž āĻšāĻ¯āĻŧāĨ¤ āĻļā§āĻˇāĻ¤ 4.2 āĻ˛āĻŋāĻāĻžā§° āĻŦāĻāĻž āĻĻā§ā§°ā§ą āĻŦāĻžāĻā§ āĻĨāĻžāĻā§āĨ¤ āĻĒāĻžāĻ¤ā§ā§°āĻā§ā§° āĻŽā§āĻ āĻ§āĻžā§°āĻŋāĻ¤āĻž āĻ¨āĻŋā§°ā§āĻŖāĻ¯āĻŧ āĻā§°āĻāĨ¤)
A. 60 L B. 78 L C. 63 L D. 72 L
Shortcut / āĻāĻŽā§ āĻĒāĻĻā§āĻ§āĻ¤āĻŋ
- 1st: Remaining after blue liquid :(āĻ¨ā§āĻ˛āĻž āĻĻā§ā§°ā§ą āĻā§°ā§ā§ąāĻžā§° āĻĒāĻŋāĻāĻ¤ āĻŦāĻžāĻā§ āĻ
āĻāĻļ) :1 - 2/5 = 3/5â
- 2nd : Remaining after black liquid: (āĻ'āĻ˛āĻž āĻĻā§ā§°ā§ą āĻā§°ā§ā§ąāĻžā§° āĻĒāĻŋāĻāĻ¤ āĻŦāĻžāĻā§ āĻ
āĻāĻļ) : 3/5 × (1 - 1/3) = 3/5 × 2/3 = 2/5 â
- 3rd : Remaining after yellow liquid: (āĻšāĻžāĻ˛āĻ§ā§āĻ¯āĻŧāĻž āĻĻā§ā§°ā§ą āĻā§°ā§ā§ąāĻžā§° āĻĒāĻŋāĻāĻ¤ āĻŦāĻžāĻā§ āĻ
āĻāĻļ) : 2/5 × (1−5/6) = 2/5 × 1/6 = 1/15â
So, the white liquid is 1/15 of the vessel. āĻ
ā§°ā§āĻĨāĻžā§ āĻŦāĻāĻž āĻĻā§ā§°ā§ą āĻĒāĻžāĻ¤ā§ā§°āĻā§ā§° 1/15â āĻ
āĻāĻļāĨ¤
Given: 1/15 = 4.2 L
Therefore, Total Capacity = 4.2 × 15 = 63 L
Ans / āĻāĻ¤ā§āĻ¤ā§° : C. 63 Litres (63 āĻ˛āĻŋāĻāĻžā§°)
Trick / āĻā§āĻļāĻ˛: Remaining fraction = Multiply all remainders (āĻŦāĻžāĻā§ āĻ
āĻāĻļ = āĻ¸āĻāĻ˛ā§ remainder āĻā§āĻŖ āĻā§°āĻ): (1 - 2/5) (1 - 1/3) (1 -5/6) = 1/15
Capacity = 4.2 × 15 = 63
Ans = 63 Litres / 63 āĻ˛āĻŋāĻāĻžā§°