### NDA Sample Paper

1) Two equal sums are lent at the same time at 4% and 3% per annum simple interest respectively. The former sum is recovered two years earlier than the latter and the amount each case is Rs. 620. Find the sum.

(a) Rs.300 (b) Rs.400 (c) Rs.5oo (d) NONE OF THESE

Ans: As the sum lent on 3% was recovered 2 years later’ therefore interest recovered in 2 years = 6%

But the sum lent at 4% secures = 1% more every year therefore 6% of the interest ( in the later sum) is compensated at

the rate of 1 % in 6÷1 =6 years

:. sum lent at 4% for 6 years and that at for 6 + 2-= 8 years

Amount in each case = Rs. 100 + 6 x 4 =Rs.124

:. principal of Rs. 124 = 100

Principal of Rs. 620 = Rs.

=Rs. 500Ans.

2) A dealer bought a horse for Rs. 800 and sold it on the same day for Rs. 927allowing the buyer a month’s credit, money being worth 4 percent per annum. What was his gain percent.

(a) 13 (b) 12 and half (c) 15 (d) NONE OF THESE

Ans: The interest on Rs. 100 in 9 months = 3/4 x 4 = Rs.3

. present value of Rs. 927 = 100/103 of 927

= Rs. 900

Gain on Rs. 800 = Rs. 900 – Rs. 800 = Rs. 100

Gain percent = .

3) A person holds Rs. 4000, % stock at SO. He transfers to % at 108. Find the change in income.

(a) RS.33.33 (b) Rs.38 (c) RS.39 (d) NONE OF THESE

Ans:(a) Stock held = Rs. 4000

Income = = Rs.100

Sale proceeds = Rs. = Rs. 3200

In come from second investment

=

Increase in income =

= Rs. 33.33 Ans.

4) A man invested Rs. 3750 in 5 percent stock at 124.75and sells out at, 120.25 with the proceeds. I buy 4.50 percent stock at Find the change in his income (Br = 1/4 % to be charged in each trasaction )

(a) Rs. 10 (b) Rs. 15 (c) Rs.20 (d) NONE OF THESE.

Ans: (b) Investment = Rs. 3750

Buying price = 124.75 + 1/4 = Rs. 125

Income = = Rs. 150

Selling price = 120.25 – 1/4 = Rs. 120

Sale proceeds = x 3750 = Rs. 3600

Buying price of the 2nd stock = Rs.

= Rs. 120

Income from the second stock = Rs.

= Rs. 135

loss in income = 150 – 135 = Rs. 15 Ans.

5) The average height of 16 men is increased by an inch of one of them measuring 4 ft. 8 inches is replaced by 2 new men, what is his height?

(a) Ht. 8 inches (b) 6 ft. (c) 7 ft.6 inches (d) NONE OF THESE

Ans: (b) Total increase in height = 1 inch x 16′

=16 inches =1 ft. 4 inches.

(Because total increase is the average increase multiplied by the number of men.) .

:. Height of the new man = 4 ft. 8 inches + 1 ft. 4 inches = 6 ft.Ans.

6) To do a piece of work B would take 3 times as long as A & C together and C twice as long as A & B together. The three men by their united exertion can complete the work in 10 days. How long would it take for each to do it himself?

(a) A = 10 days; B = 15 days; C = 18 days

(b) A =24 days; B =40 days; C = 30 days

(C) A =14 days ; B =20 days; C = 18 days

(d) NONE OF THESE

Ans: (b) The work of A & C =3 times the work of B Add the work of B to both sides

. :. the work of A, B & C = 4 times the work of B but A, B & C can complete it in 10 days

:. B can do it in 4 x 10 = 40days

Again the work of A and B = 2 times the work of C. Add the work of C to both sides ‘

The work of A, B and C =3 times the work of C. but A, Band C can do the work in 10 days

:. C can do it in 3 x 10 =30 days

Now the work of A for one day

A can do it in 120/5 =24 days Ans.

7) At what time between 8 & 10 will the hour hands of a watch coincide

(a) mts. past 9 (b) mts. past 9 (c) mts. past 9 (d) NONE OF THESE

Ans: b

8) At what time between 10 and 11 will the hands of the watch be at right angles?

(a) mts. past 10 only (b) mts. past 10 & mts. past 10

(c) mts. past 10 only (d) NONE OF THESE

Ans: b

9) Find the day of the week 01: March 20th if March 1st was Friday.

(a) Monday (b) Tuesday (c) Wednesday (d) NONE OF THESE

Ans: (b) Total number of days from March 1st to March 26th is 25 =3 weeks 4 days

The day is 4 days after Friday

:. March 26th was Tuesday

10) A starts on a cycle from a particular point at 15 km./hr. speed. After 20 minutes B starts on a cycle from the same point but at 20 km./hr. speed. At what time will B cross A

(a) 1hr. (b) hr. (c) 2 hr. (d) hr.

Ans: d

11) Of the following, the least fraction is

(a) 8.0153 (b) 8.1053 (c) 85013 (d) NONE OF THESE

Ans: a

12) The LCM of 48, 120 and 84, when reduced by 4, equals .

(a) 1680 (b) 1676 (c) 1672 (d) 1684

Ans: b

13) The LCM and , HCF of two numbers are 84 and 21 respectively. if the ratio of the two numbers is 1:4, then the larger of the two numbers is

(a) 12 (b) 48 (c) 84 (d) 108

Ans: c

14) The greatest negative integer is

(a) 0 (b) 1 (c) -1 (d) Does not exist

Ans: c

15) Which of the following cannot be the unit’s digit in a perfect square number?

(a) 9 (b) 5 (c) 7 (d) 1

Ans: c

16) The unit’s digit in the product 7 35 x 3 71 X 11 55 is

(a) 1 (b) 3 (c) 7 (d) 9

Ans: a

17) The greatest four digit number divisible by 88 will be

(a) 8888 (b) 9768 (c) 9944 (d) 9988

Ans: c

18) simplifies to

(a) 0.25 (b) 0.70 (c) 1.25 (d) 1.70

Ans: d

19) The least number that should be added to the number 7801to make it a perfect square, is

(a) 20 (b) 100 (c) 120 (d) 480

Ans: c

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