# AILET Exam Paper with Ans Keys: Section V-ELEMENTARY MATHEMATICS (NUMERICAL ABILITY)

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## AILET-DIAGNOSTIC-PAPER-FOR-LAW-ENTRANCE-TO-NLU

**Diagnostic Mock Test on AILET Pattern**

**SECTION V: **__ELEMENTARY MATHEMATICS (NUMERICAL ABILITY)__

141. Prakash, Sunil and Anil started a business jointly investing Rs 11 lakhs, Rs 16.5 lakhs and Rs 8.25 lakhs respectively. The profit earned by them in the businessat the end of three years was Rs 19.5 lakhs. What will be the 50% of Anil’s share in the profit?

(a) Rs. 4.5 lakhs (b) Rs. 2.25 lakhs

(c) Rs. 2.5 lakhs (d) Rs. 3.75 lakhs

142. Naresh purchased a TV set for Rs 11,250 after getting discount of 10% on the labelled price. He spent Rs 150 on transport and Rs 800 on installation. At what price should it be sold so that the profit earned would have been 15% if no discount was offered?

(a) Rs 12937.50 (b) Rs 14,030

(c) Rs 13,450 (d) Rs 15,467.50

143. Mr Duggal invested Rs 20,000 at the rate of 20 per cent per annum. The interest was compounded half yearly for first one year and in the next year it was compounded yearly. What will be the total interest earned at the end of two years?

(a) Rs 8,800 (b) Rs 9,040

(c) Rs 8,040 (d) Rs 9,800

144. In how many different ways can the letters of the word DESIGN be arranged so that the vowels are at the two ends?

(a) 48 (b) 72

(c) 36 (d) 24

145. Out of 5 men and 3 women, a committee of 3 members is to be formed so that it has 1 woman and 2 men. In how many different ways can it be done?

(a) 20 (b) 10

(c) 23 (d) 30

146. 8 men and 4 women together can complete a piece of work in 6 days. Work done by a man in 1 day is double the work done by a woman in 1 day. If 8 men and 4 women started working and after 2 days, 4 men left and 4 new women joined. In how many more days will the work be completed?

(a) 5 days (b) 8 days

(c) 6 days (d) 4 days

147. Mr Giridhar spends 50% of his monthly income on household items and out of the remaining he spends 50% on transport, 25% on entertainment, 10% on sports and the remaining amount of Rs 900 is saved. What is Mr Giridhar’s monthly income?

(a) Rs. 6,000

(b) Rs. 12,000

(c) Rs. 9,000

(d) cannot be determined

148. A sum of money is divided among *A*, *B*, *C *and *D *in the ratio of 3 : 4 : 9 : 10. If the share of *C *is Rs 2,580 more than the share of *B*, what is the total amount of money of *A *and *D *together?

(a) Rs 5,676 (b) Rs 6,192

(c) Rs 6,708 (d) Rs 7,224

149. If the numerator of a fraction is increased by 20% and the denominator is increased by 25%, the fraction obtained is 3/5. What was the original fraction?

(a) 5/7 (b) 4/7

(c) 3/8 (d) none of these

150. The compound interest accrued on an amount of Rs 25,500 at the end of three years is Rs 8,440.50. What would be the simple interest accrued on the same amount at the same rate in the same period?

(a) Rs 4,650 (b) Rs 5,650

(c) Rs 6,650 (d) Rs 7,650

**ANSWERS AND EXPLANATIONS**

**1. **(d) **2. **(a)

**3. **(b) **4. **(c)

**5. **(d) **6. **(c)

**7. **(a) **8. **(b)

**9. **(d) **10. **(a)

**11. **(b) **12. **(d)

**13. **(a) **14. **(c)

**15. **(d) **16. **(a)

**17. **(d) **18. **(c)

**19. **(b) **20. **(b)

**21. **(a) **22. **(a)

**23. **(d) **24. **(a)

**25. **(d) **26. **(c)

**27. **(a) **28. **(b)

**29. **(c) **30. **(a)

**31. **(c) **32. **(b)

**33. **(d) **34. **(b)

**35. **(c) **36. **(c)

**37. **(a) **38. **(a)

**39. **(d) **40. **(a)

**41. **(b) **42. **(d)

**43. **(c) **44. **(a)

**45. **(a) **46. **(d)

**47. **(b) **48. **(d)

**49. **(a) **50. **(b)

**51. **(b) **52. **(d)

**53. **(d) **54. **(a)

**55. **(c) **56. **(a)

**57. **(a) **58. **(c)

**59. **(b) **60. **(d)

**61. **(c) **62. **(b)

**63. **(c) **64. **(a)

**65. **(b) **66. **(c)

**67. **(d) **68. **(a)

**69. **(d) **70. **(c)

**71. **(b) **72. **(c)

**73. **(b) **74. **(b)

**75. **(a) **76. **(c)

**77. **(a) **78. **(b)

**79. **(b) **80. **(c)

**81. **(a) **82. **(b)

**83. **(b) **84. **(b)

**85. **(b) **86. **(a)

**87. **(a) **88. **(a)

**89. **(c) **90. **(b)

**91. **(c) **92. **(a)

**93. **(d) **94. **(a)

**95. **(b) **96. **(c)

**97. **(c) **98. **(d)

**99. **(a) **100. **(c)

**101. **(d) **102. **(b)

**103. **(a) **104. **(a)

**105. **(b) **106. **(d)

**107. **(a) **108. **(b)

**109. **(c) **110. **(a)

**111. **(b) **112. **(a)

**113. **(d) **114. **(b)

**115. **(b) **116. **(b)

**117. **(a) **118. **(a)

**119. **(d) **120. **(a)

**121. **(b) **122. **(d)

**123. **(d) **124. **(b)

**125. **(d) **126. **(b)

**127. **(c) **128. **(a)

**129. **(b) **130. **(d)

**131. **(a) **132. **(c)

**133. **(c) **134. **(b)

**135. **(d) **136. **(c)

**137. **(a) **138. **(d)

**139. **(d) **140. **(d)

**141. **(b) **142. **(d)

**143. **(b) **144. **(a)

**145. **(d) **146. **(a)

**147. **(b) **148. **(c)

**149. **(d) **150. **(d)

**SECTION V: ELEMENTARY MATHEMATICS (NUMERICAL ABILITY)**

141. (b) Profit will be shared in the ratio of

11 × 3 : 16.5 × 3 : 8.25 × 3

= 11 : 16.5 : 8.25 = 44 : 66 : 33

Anil’s share in the profit:

33/143 × 19.5 = 4.5 lakhs

50% of Anil’s share = 2.25 lakhs.

142. (d) Cost price of TV when discount is not offered = 11250 × 100/90

= Rs 12500

Total cost of TV after transport and installation = 12500 + 800 + 150 = 13450. To earn 15% profit, he must sell at 13450 × 115/100

= Rs 15467.50.

143. (b) Interest earned in 1st half of a year

= 20,000 × 10/100 = 2000

Similarly, during second half, interest earned = 2200

During second year, interest earned = 4840 (*Note*: Interest is calculated as compound)

144. (a) Required no. of ways

= 2P2 × 4P4 = 48

145. (d) Required no. of ways

= 3C1 × 5C1 = !! × !!! = 30

146. (a) Let work done by 1 man in 1 day

= 2x

work done by 1 woman in 1 day = x

8 men and 4 women together can complete a piece of work in 6 days

Work done by 8 men and 4 women in 1 day = 1/6

=> 8 × 2x + 4x = 1/6

=> 20x = 1/6

=> x = 1/120

8 men and 4 women worked for 2 days. Work completed = 1/6 × 2 = 1/3

Pending work = 1−1/3 = 2/3

Then 4 men left and 4 new women joined them

*i.e.*, 4 men and 8 women worked and completed the work. Work done by 4 men and 8 women in 1 day = 4 × 2x + 8 × x

= 16x = 16/120 = 2/15

Required number of days

= (2/3) / (2/15) = 5 days

147. (b) Let the total monthly income be Rs x. After spending 50% remaining is Rs x/2, After spending (50% + 25% + 10%) of x/2, Remaining is

x/2 – (x/2 × 85%) = 900 (given)

x/2 – 85/200x = 900 (given)

x = 12000.

148. (c) Let the sum of money be x

*B*’ share = 4/26x. *C’s *share = 9/26x

*C*’s share – *B*’ share = 2580

i.e. 9/26x – 4/26x = 2580 x = 516

Therefor, A’s share = 516 × 3 = 1548

D’s share = 516 × 10 = 5160

A + D = 1548 + 5160 = 6708

149. (d) The multiplier for a 20% increase is 1.20, for 25% increase is 1.25

Let n = the original numerator

Let d = the denominator

1.2n = 3 n = 3/1.2

n = 2.5 and 1.25d = 5

d = 5/1.25 d = 4

2.5/4 but the numerator has to be an integer, mult by 2/2

2.5/4 × 2/2 = 5/8 is the original fraction

150. (d) Total amount after three years = 25500 + 8440.50 = Rs. 33940.50

Thus

[(100 + r) / 100] ^3

= 33940.50/25500 = 1.331

Thus, r = 10%

So the simple interest will be

[25500 × 3 × 10) / 100] = Rs 7650

*Note: *For this type of question we need to apply our common sense. We can see that 8440.50 is more than 30% of 25500. This implies that the rate of interest may be 10% (for one year). Now check whether this is true or not. At 10% rate of compound interest for 3 years the equivalent simple rate of interest is 33.1%, so 33.1% of 25500 should be equal to 8440.50. And this is true. So our conclusion is correct.