Night Class: Quant Quiz

1. Anil and Deepak started a business by investing Rs. 24000 and Rs. 36000 respectively. At the end of 5th month from the start of the business, Sohan joined them with Rs. 16000. At the end of 7th month Deepak quits, at that time Sohan invests Rs. 4000 more. At the end of 10th month, Deepak rejoins with the same investment. If the profit at the end of the year is Rs. 26164, what is Deepak’s share of profit?
1) Rs. 10894
2) Rs. 10394
3) Rs. 10000
4) Rs. 11394
5) Rs. 11000

2. The circumference of the two circles is 352 cm and 264 cm respectively. What is the difference between the area of the larger circle and the smaller circle?
1) 4032 cm^2
2) 4332 cm^2
3) 4312 cm^2
4) 4123 cm^2
5) 4132 cm^2

3. The price of sugar is increased by 28%. Therefore a family reduces its consumption so that the increment in the expenditure of sugar is only 20%. If the consumption of sugar is 15 kg before the increment, what is the consumption now?
1) 15 1/16 kg
2) 14 1/16 kg
3) 14 3/16 kg
4) 14 1/18 kg
5) 15 1/8 kg

4. One–third of Radha’s savings in National Savings Certificate is equal to one–half of her savings in Public Provident Fund. If she has Rs. 150000 as total savings, how much has she saved in Public Provident Fund?
1) Rs. 60,000
2) Rs. 75,000
3) Rs. 80,000
4) Rs. 90,000
5) Rs. 85,000

5. The number obtained by interchanging the digits of a two-digit number is less than the original number by 54 if the digit at the unit place of the original number is one–third of the digit at ten’s place. What is the original number?
1) 31
2) 93
3) 62
4) 26
5) 39

6. The present age of Raju and his father are in the ratio of 2 : 5. Four years hence, the ratio of their ages will become 5 : 11. What was the father’s age five years ago?
1) 35 years
2) 40 years
3) 36 years
4) 38 years
5) 42 years

7. The number obtained by interchanging the two digits of a two-digit number is less than the original number by 36. If the sum of the two digits of the number is 8, then what is the original number?
1) 26
2) 53
3) 62
4) 35
5) 71

8. The distance between two stations S1 and S2 is 640 km. A train J starts at 5 pm from S1 and moves towards S2 at an average speed of 80 km/h. Another train K starts from S2 at 4 : 20 pm and moves towards S1 at an average speed of 100 km/hr. How far from S1 will the two trains meet?
1) 248.18 km
2) 278.48 km
3) 276.38 km
4) 254.81 km
5) 268.18 km


9. Aashi had Rs. 20,000 with her out of this money she lent some money to Anshul for 4 years at 20% p.a. simple interest. She lent the remaining money to Rajat for an equal number of years at the rate of 24% p.a. After 4 years, Aashi found that Anshul had given her Rs. 864 more as interest as compared to Rajat. The amount of money which Aashi had lent to Rajat must be.
1) Rs. 10,600
2) Rs. 11,400
3) Rs. 8600
4) Rs. 10,400
5) Rs. 9600

10. A 280-m-long train takes 20 sec to cross a person who is going in the same direction with the speed of 6 km/h. After crossing that person, the train can reach next station in 45 min. How long will that person take to reach the station after being crossed by train?
1) 7 hr 3 min
2) 6 hr 3 min
3) 7 hr 30 min
4) 7 hr 50 min
5) 6 hr 30 min

Answers

1. 4;
Ratio of profit Anil, Deepak and Sohan
= 24000 × 12 : 36000 × 7 + 36000 × 2 : 7 × 16000 + 4000× 5
= 288 : 324 : 132
= 72 : 81 : 33
= 24 : 27 : 11
Deepak’s share of profit = 27/62 * 26164 = Rs. 11,394

2. 3;
r1 = 264 * 7/44 = 42cm
r2 = 352 * 7/44 = 56cm
Reqd difference = 22/7[(56)^2 – (42)^2] = 22/7 * 98 * 14 = 4312

3. 2;
Let the price of sugar before increase be ` x
Consumption = 15 kg
Expenditure on sugar = 15x
After increase
Expenditure on sugar = 120% of 15x = 18x
Price of sugar = 128% of x = 32x/25 per kg
New Consumption = 18x*25/32x = 14 1/16kg

4.1;
 Let Radha’s savings in National Savings Certificate be x.
Then, according to the question,
x/3 = 1/2(150000 – x)
2x = 450000 – 3x
x = Rs. 90,000
Saving in Public Provided Fund
= 1, 50,000 – 90,000 = Rs. 60,000

5. 2;
Let the two-digit number be 10x + y
Numbers obtained by interchanging the digits = 10y + x
According to the question,
10x + y – (10y + x) = 54
9x – 9y = 54  x –y = 6 … (i)
Again, y = x/3
3y = x
From (i) and (ii)
y = 3 and x = 9
Required number is 93

6. 1;
Let the present age of Raju and his father be 2x and
5x respectively.
Hence, (2x + 4)/(5x + 4) = 5/11
22x + 44 = 25x + 20
3x = 24
x = 8
Father’s age 5 years ago = 5 × 8 – 5 = 35 years

7. 3
Let the original number be 10x + y
(10x + y) – (10y + x) = 36
9x – 9y = 36
x – y = 4 and x + y = 8
x = 6; y = 2
The original number = 62

8. 4
Let two trains meet at x km from station S1
Time taken by K to cover (640 – x) km – Time taken by J to cover x km.= 40/60 = 2/3
  (640 – x)/100 – x/80 = 40/60
x = 6880/27 = 254.81 km

9. 3
Let the money lent to Anshul be Rs. x
Then, money lent to Rajat = (20000 – x)
SI for Anshul = x * 20 * 4/100 = 20x/25
SI for Rajat = (20000 – x) * 24 * 4/100
According to the question,
20x/25 – (20000 – x) 24/25 = 864
x = 11400
Amount lent to Rajat = Rs. (20000 – 11400) = Rs. 8600

10. 1;
Speed of the person = 6 km/hr
= 6 * 5/18 = 5/3 m/s
Let the speed of train be x m/s
20 = 280/(x – 5/3)
x – 5/3 = 14
x = 47/3m/s
Now the distance covered by train in 45 minutes.
= 47/3 * 60 * 45 = 42300
Time taken by person to cover the distance
= 42300/(6*5/18) = 25380 sec
25380/(60 * 60) = 7 hours 3 minutes