Mixed Questions on Quantitative Techniques for CLAT 2020

Mixed Questions on Quantitative Techniques for CLAT 2020

  • A boat​​ named Naav​​ covers a distance of 96 km in 6 hours and​​ its speed in still water is 13 km/h. Calculate the time it will take to cover 96kms in​​ upstream?

  • Angad runs a distance of 60 km in 12 hour and runs back the same distance in 5 hours. Calculate the average speed/.

  • How long will it take a train​​ of 250​​ m travelling at the speed of 100 km/h to overtake a 150 m long train running at the speed of 50 km/hr?

  • Akash gave a loan of Rs. 10000 to Aman for 3 years and Rs. 5000 to Arshit for 2 years on simple interest. If the rate of interest was same and he received a total of Rs. 5000 as interest from both of them, calculate the rate of interest.

  • Find the time taken by X to cover a distance of​​ 225 km at the speed of 20 km/h.

  • Asmita took a loan of Rs. 5000 on simple interest and at the end paid an interest of Rs. 1000. If the rate of interest and the number of years for which loan is taken is equal, calculate the rate of interest.

  • Find the principle amount if the total​​ amount received​​ after 2​​ years at the compound interest rate of 10% is Rs. 2000.

  • If 15% of​​ 200 is x % more than 10% of 100. Find the value of x.

  • If the price of garments is decreased by 16%, what percent of more garment must be bought to keep the expenditure unchanged?

  • Ankush’s salary was first reduced by 20% and then increased by 25%. Calculate the total gain/loss percentage.

  • Amish​​ suffered a loss of Rs. 20% of the money he invested and then spent 60% of the remainder and now he is left with Rs. 2000. Calculate the money he had in the beginning.

  • If the​​ 2500 is more than 2000 by 25 %, by what percent is 2000 less than 2500?

Solution:​​ Required Percentage = (500/2500)*100 = 20%

  • For how many years was the money lent, if the interest received at​​ simple interest of​​ 10% per annum for Rs. 7000 is Rs. 2800?

  • Calculate the difference in amount of SI and CI for an amount of Rs. 15000 lent at 15% per annum for 2 years.

  • Find the ratio of the SI earned in same amount of money at same rate of interest for​​ 3​​ years and 10 years.

 ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​​​ 

Answers with explanation

  • ​​ Downstream speed = 96/6 = 16 km/h

Let the speed of the boat in still water be x km/h and speed of the stream be y km/h.

x = 13 km/h

Therefore, Downstream speed = (x+y) km/hr

 ​​ ​​ ​​ ​​​​ 16 = 13+ y

y = 3 km/h

Upstream speed of Naav = (x-y) km/h

 ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​​​  ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​​​ = 13 -3 = 10 km/h

Required time = 96/10 = 9.6 hours

 

  • Total distance = 60 * 2 = 120 km

Total time taken = 12+ 5 = 17 hours

Average speed = 120/17 = 7.05 km/h

 

  • Total distance = 250 + 150 = 400 m

Relative speed = 100- 50 = 50 km/hr = 13.8 m/sec

Time taken= 400/ 13.8 = 28.9 seconds

 

  • For Aman

SI1​​ = PRT/100

 ​​ ​​ ​​ ​​ ​​​​ = (10000*R*3)/ 100

 ​​ ​​ ​​ ​​​​ = 300R

For Arshit

SI2​​ = PRT/100

 ​​ ​​ ​​ ​​ ​​​​  ​​ ​​ ​​ ​​​​ = (5000*R * 2)/100​​ 

 ​​ ​​ ​​ ​​​​ ​​ = 100 R

SI1​​ + SI2​​ = 5000

400R = 5000

R = 5000/400

 ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​​​ ​​ = 50/4 = 12.5%

  • Time = Distance / Speed

 ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​​​ = 225/20

 ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​​​ = 45/4

 ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​​​ = 11.2 km/h

 

  • SI = PRT/100

 ​​​​ 1000 = (5000*R*T)/ 100

Since R = T

1000 = 50 R2

R2​​ = 1000/50 = 20

R = 4.4%

 

  • A = P*(1+r/100)]​​ n

2000 = P* [1+ (10/100)]​​ 2

​​ 2000 = P (121/100)

 ​​ ​​​​ P = (2000* 100)/121

 ​​ ​​ ​​ ​​​​  ​​​​ = Rs. 1652 (approx...)

 

  • 15% 0f 200 = (15/100)*200 = 30

​​ 10% 0f 100 = (10/100)*100 = 10

 ​​​​ x = (20/10)*100 = 200%

 

  • Here, the price has reduced by 16%, and therefore,

Percent of garment more that should be bought in order to keep the expenditure unchanged =​​ [m/ (100-m) *100] %

 ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​​​ = [16/ (100-16)*100]

 ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​​​ = 19.04%

 

  • Let the original salary be Rs. x.

Reduced salary = x – (20/100)*x

 ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​​​ = x – x/5

 ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​​​ = 4x/5

Increased salary = 4x/5 + (25/100)*(4x/5)

 ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​​​ = (4x/5) + (1/4)*(4x/5)

 ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​​​ = (4x/5) + (x/5)

 ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​​​ = x

Therefore, no difference.

 

  • : Let the money at the beginning be Rs. x.

Money left after loss = x – (20/100)*x = x – x/5​​ 

 ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​​​ = 4x/5

Money left after spending = (40/100)*(4x/5)

 ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​​​ = (2/5)*(4x/5)

 ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​​​ = 8x/25

8x/25 = 2000

X = (2000*25)/8

 ​​ ​​ ​​​​ = Rs. 6250

 

  • Required Percentage = (500/2500)*100 = 20%

 

  • SI = PRT/100

​​ 2800 = (7000*10*T)/100

2800 = 700T

​​ T = 4 years

 

  • SI = PRT/100

 ​​ ​​ ​​ ​​​​ = (15000*15*2)/100

 ​​ ​​ ​​ ​​ ​​ ​​​​ = 2250 *2 = Rs. 4500

A = P [1+(r/100)]​​ n

 ​​ ​​ ​​ ​​ ​​​​ = 15000 [1+ (15/100)]​​ n

 ​​ ​​ ​​​​ = 15000 [(23/20)*(23/20)]

 ​​ ​​ ​​ ​​​​ = [(150*23*23)/4]

 ​​ ​​ ​​ ​​ ​​​​ = Rs. 19837.5

CI = 19837.5 – 15000 = Rs. 4837.5

Difference = Rs. 337.5

 

  • SI1​​ = PRT/100

 ​​ ​​ ​​ ​​ ​​​​ = 3PR/100

 ​​ ​​ ​​ ​​​​ SI2​​ = PRT/100​​ 

 ​​ ​​ ​​ ​​ ​​ ​​​​ = 10PR/100

 ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​​​ = PR/10

Required Ratio = (PR/20)/ (PR/10)​​ 

 ​​ ​​ ​​ ​​ ​​ ​​ ​​​​  ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​ ​​​​ = 3:10

 

 

 

 

 

 

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