**Find solutions for all the questions at the end of each set:**

### Set A

1. A 4-digit number is formed by repeating a 2-digit number such as 2525, 3232, etc. Any number of this form is always exactly divisible by

(1) 7

(2) 11

(3) 13

(4) Smallest 3-digit prime number

2.A number when divided by 6 leaves remainder 3. When the square of the same number is divided by 6, the remainder is :

(1) 0

(2) 1

(3) 2

(4) 3

3.The number 1, 2, 3, 4,…………..1000 are multiplied together. The number of zeros at the end (on the right) of the product must be

(1) 30

(2) 200

(3) 211

(4) 249

4.The average age of 11 players of a cricket team is increased by 2 months when two of them aged 18 years and 20 years are replaced by two new players .The average age of the new players is :

(1) 19 years 1 month

(2) 19 years 9 month

(3) 19 years 11 month

(4) 19 years 5 month

5.The sum of the H.C.F. and L.C.M of two number is 680 and the L.C.M. is 84 times the H.C.F. If one of the numbers is 56, the other is :

(1) 84

(2) 12

(3) 8

(4) 96

6.A reduction of 33 1/3% in the price of an item would enable a purchaser to get 4 more a rupee. The price before reduction was :

(1) 2 per rupee

(2) 4 per rupee

(3) 12 per rupee

(4) 8 per rupee

7.Rs. 68000 is divided among A, B and C in the ratio of 1/2 ∶ 1/4 ∶ 5/16 , The difference of the greatest and the smallest part is :

(1) Rs. 6000

(2) Rs. 14440

(3) Rs. 9200

(4) Rs. 16000

8.The difference between simple and compund interest on a certain sum of money for 2 years at 4 per cent per annum is Rs. 1. The sum of money is :

(1) Rs. 600

(2) Rs. 625

(3) Rs. 560

(4) Rs. 650

9.The cost of manufacturing an article was Rs. 900. The trader wants to gain 25% after giving a discount of 10%. The marked price must be :

(1) Rs. 1500

(2) Rs. 1250

(3) Rs. 1200

(4) Rs. 1000

10.A and B together can do a work in 8 days, B and C together in 6 days while C and A together in 10 days, if they all work together, the work will be completed in :

(1) 3 3/4 days

(2) 3 3/7 days

(3) 5 5/47 days

(4) 4 4/9 days

Answers and solution:

1.(4) Let the unit digit be x and ten’s digit be y.

∴ Number

= 1000y + 100x + 10y + x

= 1010y + 101x = 101 (10y + x)

Clearly, this number is divisible by 101, which is the smallest three-digit prime number.

2.(4) The remainder will be same.

On dividing 9 by 6, reminder = 3

On dividing 81 by 6, remainder = 3

3.(4) Zeros are obtained if there is any zero at the end of any multiplicand and if 5 or multiply of 5 are multiplied by any

even number i.e(5)^n(2)^m has n zeros if n <m or zeros if m<n

Now ,we obtain the index of 5 as follows:

Index = (1000/5) + (1000/5^2) + (1000/5^3) + (1000/5^4)

= 200+40+8+1 = 249

4.(3) Total age increased

= 11×2=22 months

Total age of new players

= (18 + 20) years + 22 months

= 39 years 10 months

∴ Their average age

= (39 years 10 months)/12

= 19 years 11 months

5.(4) Let HCF be h and LCM be l.

Then, l = 84h and l + h = 680

=> 84h + h = 680

=> h = 680/85=8

∴ l = 680-8 = 672

∴ Other number

= (672×8)/56=96

6.(4)

7.(4) Ratio = 1/2 ∶ 1/4 ∶ 5/16

= 8 : 4 : 5

Sum of ratios = 8 + 4 + 5 = 17

∴ Required answer

= Rs. ((8-4)/17)×68000

= Rs. 4/17×68000

= 16000

8.(2)

9.(2) CP = Rs. 900

∴ S.P. = 125% of 900

= Rs. ((900×125)/100)

= Rs. 1125

Let the marked price be Rs. x

∴ 90% of Rs. x = Rs. 1125

=> x = (1125×100)/90=Rs.1250

10.(3)

**Find solutions for all the questions at the end of each set:**

### Set B

1.Determine the selling price (in rupees) if the list price is Rs. 1,000 and the two successive discounts are 30% and 20%.

(1) 700

(2) 140

(3) 560

(4) 600

2.An item costing Rs. 300 is being sold at 10% gain. If the selling price is reduced by 15%, what will be the gain or loss per cent ?

(1) 6 1/2% gain

(2) 6 1/2% loss

(3) 5% loss

(4) 5% gain

3.What is the least number to be added to 920 to make it a perfect square ?

(1) 31

(2) 41

(3) 39

(4) 49

4.If the price of an article increases at the rate of 8% perannum, what will an article cost, at the end of two years, if its present price is Rs. 20,000?

(1) Rs. 23,328

(2) Rs. 22,238

(3) Rs. 21,218

(3) Rs. 20,124

5.The ratio of three numbers is 2 : 3 : 5 and their product is 10290. The numbers respectively are

(1) 35, 21, 14

(2) 21, 14, 35

(3) 14, 21, 35

(4) 14, 35, 21

6.4 men and 6 women can complete a work in 8 days, while 3 men and 7 women can complete it in 10 days. The ratio of the daily work done by a man and a woman is

(1) 11 : 1

(2) 7 : 4

(3) 5 : 3

(4) 9 : 8

7.X invested Rs. 200 more than Y in a business. If X invested his money for 5 months and Y for 4 months, and X gets Rs. 90 more than Y out of a profit of Rs. 510, how much did Y invest ?

(1) Rs. 1,600

(2) Rs. 1,500

(3) Rs. 1,400

(4) Rs. 1,300

8.If the interest period is 3 months, then the compound interest on Rs. 15,000 for 9 months at 8% per annum is

(1) Rs. 981.21

(2) Rs. 918.12

(3) Rs. 918.21

(4) Rs. 980.12

9.A person wants to divide a sum of Rs. 3,90,300 between his two sons who are 13 and 15 years of age respectively in such a way that their shares, if invested at 4% per annum compound interest, should produce the same amount when they become 18 years of age. Find the share of the elder son.

(1) Rs. 202810

(2) Rs. 202800

(3) Rs. 202081

(4) Rs. 202815

10.A sum of money at simple interest amounts to Rs. 9,440 in 3 years. If the rate of interest is increased by 25%, the same sum of money amounts to Rs. 9,800 in the same time. Find the rate of interest.

(1) 4% per annum

(2) 6% per annum

(3) 8% per annum

(4) 10% per annum

Answers and Solution:

1(3)

Single equivalent discount = ((30+20-(30×20)/100)) = 44%

so Selling price of article = (100 – 44)% of 1000

= 56×1000/100

= 560

2.(2)

sp of article = 300×110/100

= 330

again after discount 15% then,

sp = 330x(100-15)/100

= 330×85/100

= 280.50

loss = 300-280.5

= 19.5

percent loss = 19.5/300×100 => 6.5%

3.(2)

4.(1)

5.(3)

6.(1) Ratio of man and woman => 4×8 men + 6×8 women = 3×10 men + 7 x 10 women

=> 32 men + 48 women = 30 men + 70 women

=> 2 men = 22 women

=> 1 men = 11 women

Required ratio : 11 : 1

7.(3)

8.(2) Rate of intrest = 2 % per quarter

Time 3 quarter

so C.I = p(1+r/100)^t-1

= 15000(1+8/100)^3-1

= 15000 x 0.612

= 918.2

9.(3)

10.(2)