SSC MAINS Quant Solution. S7. Ans. (d) Speed of A Speed of B = 5 7 = 5 7. S8. Ans. (a); = tan. = tan 2. = tan 2 +tan +1. S10. Ans.

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1 SSC MAINS Quant Solution S. Ans. (a) a 4 a 0, b andc a + b + c 0 S. Ans. (a) Let the speed of cyclist km/h Relative speed 6 km/h km\hr S. Ans. (b); + b + c So time taken to travel 4 km 0 min Distance b/w C & D km 0 Total distance km S6. Ans. (c)the required factor is- (a+b-c)(b+c-a)(c+a-b) S7. Ans. (d) Speed of A Speed of B S8. Ans. (a); Distance travel by A Distance travel by B Time taken to fill rd tank hrs. Now work done due to leak Now time taken to fill 40 hrs 0 Total time taken 6 hrs S4. Ans. (b) Let cost price of table T & C.P. of Chair C 5 T + 5 C 0 C T.(i) & 5 T 5 C 5 6T 4C (ii) From (i) & (ii) T 60 Rs S5. Ans. (a) Original time taken to travel B to D 5 05 min If accident takes place after 4 km than original time to travel C to D 5 75 min Req. Ratio 5 : S9. Ans. (d); tan + cot cot tan + tan tan tan tan tan + tan tan tan tan tan tan tan S0. Ans. (d); tan tan (tan ) tan +tan + tan tan + cot + + +cot sin + cos + sin sin + cos +tan + sin? S. Ans. (c); amount of milk left lit S. Ans. (d) CP of 0 cycles Rs Cost on repair 000 Rs Total epense 7000 Rs total S.P Page

2 Rs Loss % 5 7 % 70 7 S. Ans. (c) Ratio of speed 4 5 Ratio of time 5 4 Difference of time 60 min Actual difference 6 min Actual time taken with speed of 40 km/h 0 min Correct time 0 9 min S4. Ans. (d) Let sum Rs S5. Ans. (c) Ratio of distance covered on two days 4 5 distance covered on first day 56 km Req. Ratio 4 : 56 : 4 S6. Ans. (c) Cos0 b AD AD b Sin 75 a AD a b a b S7. Ans. (b)requiredans is- Twice the distance between the centroid and the circumcentre. S8. Ans. (c) Let the two equal sides be a cm. In 5 days work done 5 work 6 days 9 work Sol. In 6.5 days 40 work will be done S0. Ans. (c) a + b + c a b c a + b + + c + 0 a, b, c Sol. a b + c + S. Ans. (d) Sol S. (d); Percentage of milk in vessel A 800 % Percentage of milk in vessel B 500 % 7 : 7 S. Ans. (d) length 6 cm Breadth cm height 6 cm Circumference πr cm r 7 cm Volume πr h cm³ 7 S4. Ans. (a) Each edge 0 m Volume Area height Where area 0 0 h v m S5. Ans. (d) AC a Sol. Ratio of ABE and ACD a S9. Ans. (b) a A + B + C does work in days 7 work + β +γ b a β + β γ + γ c a β γ d a Now, ² + β² + γ² + ( β +βγ + γ) ( +β +γ)² ² + β² + γ² + c a b a + β + γ b ac a b Page a

3 S6. Ans. (b) a b + a + b y a ab b a + b + (a + b)y a + b ii (ii) b ab b b a + b a + b b a + b from (ii) y ab a+b S7. Ans. (a).(i) (ii) S. Ans. (b) Discount % S. Ans. (c) % In ABC, we have PQ AC AB CB AP CQ AB CQ BC AP S8. Ans. (d) 5 CDE + DCE DCE 45 & AEB + BEC 80 AEB AEB 65 S9. Ans. (a) Cot 0 AC AB AC h & cot 45 AD AB AD h ( h h)units travelled in min hunits travelled in h h h 6( + ) 6.9min 6 min sec S0. Ans. (a) Let h rise in water surface h h cm S. Ans. (c) S4. Ans. (d) ABC ~ APQ AB AP BC PQ BC PQ PQ : BC : S5. Ans. (c) S6. Ans. (b) of of By C & D S7. Ans. (c) v u v+u & 5 v u + 5 v+u from (i) & (ii) u 4km/h S8. Ans. (c) α + β + γ Page.(i). (ii)

4 Sum of money at compound interest becomes times in 5 years It will become 8 times i.e ()³ times in 5 5 years S9. Ans. (b) Let the share of elder and younger sons be andrs(00 ) respectively amount got by elder son amount got by younger son Rs 6400 Thus, younger son s share Rs Rs S40. Ans. (d) p a + b S4. Ans. (b) X Y X + Y XY * ² + ² S4. Ans. (c) Let M.P. of a shirt and trouser 00 & 00 S.P. of shirt discount on shirt 60 & total discount 0% req % % S4. Ans. (d); AB BC CA a cm Area of ABC 4 4a Area of sectors of a a Area of shaded region area of ABC area of sectors a a ( )a cm S44. Ans. (a) Remainder S45. Ans. (b) Relative speed km/h 0.88km/h m/s 8 Req. time sec min 8 S46. Ans. (b) AOC [ ] 40 S47. Ans. (c) On the second year (in terms of CI) is P + P + P Page % S48. Ans. (d) Total of 64 innings 968 let highest score lowest score 80 total of 6 innings ecluding these two 70 sum of these two innings S49. Ans. (c) Total of 8 no. 60 A.T.Q Sum of first Sum of net 7 & let sith no. Seventh no. + 4 & eighth no eighth no

5 S50. Ans. (c) Total height of 40 students 650 total of 7 students 5994 & A + B + C 56 A.T.Q A + A + (A ) 56 A 58 A 76 cm S5. Ans. (d) Ratio of milk and water in two vessles Req ratio : 7 S5. Ans. (a) A.T.Q a + y b z c a sec θ. cos ϕ a + b sec θ. sin ϕ c tan θ b c Sec²θ. Cos² ϕ + Sec²θ.Sin² ϕ tan²θ Sec²θ (Cos²ϕ +Sin²ϕ) tan²θ Sec²θ tan²θ S5. Ans. (d) Let the radius be r, then difference in the distance πr r r π r 7 60 r 5 m S54. Ans. (d) One days wages of both So the same money in sufficient to pay days wages of both S55. Ans. (a) CP 0 0 SP Profit % % S56. Ans. (b) a + b + c ab bc ca 0 a + b + c ab ac ca 0 a b + b c + c a 0 a b c a+c b b b S57. Ans. (a) + y z z y z z y z z y S58. Ans. (d) + z z z y z z z y z +, so + 6 z z S59. Ans. (b) S.P. for a profit of % 8000 Rs.8960 Discount Rs. Rs 8960 Rs 40 S60. Ans. (c) Discount % 8 S6. Ans.(a) % In O M B O M 5 44 O M In O N D O N 5 ON 5 M N O M + O N cm. S6. Ans.(c) S6. Ans.(b) BPC 90 A Area of A O E 5 cm Area of quadrilateral B D O F 5 cm 0 cm Page 5

6 S64. Ans.(c) Area of verandah Cost of flooring the verandah Rs. S65. Ans.(b) AD : BC : BE 0 cm Area of A B C D A D+B C B E B C 8 cm. In OBC OAD Area of OBC 80 sq.m. S66. Ans.(c) [ ] 4 Cube 64 S67. Ans.(c) + y + z y + yz + z + y + z y yz z 0 ( + y + z y yz z 0 + y + y + z + z + y yz z 0 y z Thus the is equilateral. S68. Ans.(d) M.P. 480 Discount 0% SP. Rs. 4 CP. 4 Rs Req % 80 0% 400 S69. Ans.(d) a b, c d, e f a + c + 4e 9 b + d + 4f S70. Ans.(c) Rs. 00 Interest Rs r r 0% S7. Ans.(b) a a n n (659 7) + 64 Sum n (a + a n ) 64 (9 + ) S7. Ans.(a) A P + r 840 P + & 96 P + t r r 4 (i) 5 (ii) Dividing (ii) and (i) r 840 r.5% S7. Ans.(c) Transverse common tangent d r + r S74. Ans.(b) Total no. of Bricks S75. Ans.(c) X.. X + X + X X cm. X 9 4 S76. Ans.(c) AOE 50 & DAO 5 EOB OE OB OEB OBE CBE S77. Ans.(d) Area of base Perimeter In radius 5 45 cm Volume of Prism Area of Base height height Height cm. S78. Ans.(c) Angle b/w hour hand and minute hand at : 0 am min 0 hour M 0 5 ATQ, 5 M 0 M 0 Angle will be double at : 9 am. S79. Ans.(a) Amount received by a boy P Amount received by a girl 50 P If all students are girls then money needed 57.5 Rs Page 6

7 If all students are boys then money needed 5 Rs. No. of girls in class S80. Ans.(a) Length of wall 5 height of wall m Sum of length and height of wall 7 cm. S8. Ans.(b) So length of longest parallel side 9 7 cm S8. Ans.(a) Let side Area of square Area of rhombus Sin 60 Ratio S8. Ans.(b) Let distance be D km. D D 6 4 D D D.6 km. S84. Ans.(b) A + B 5 A B 5 A 75 & B 60 S85. Ans.(c) Sin BAD Sin π AD Sin BAD (i) AD Sin CAD (ii) AD From (i) & (ii) Sin BAD 6 Sin CAD 6 6 S86. Ans.(a) Sin A Cos (A 6 ) A 9 S87. Ans.(d); Epects to reach 00 kms in 4 hrs.but after hrs he had completed only 0 kms (40%) So he has to cover 80 kms more in hrs So initial speed 0 60 kmph. Final sped to reach in time kmph Increase in speed kmph. S88. Ans.(c) a (sin θ + cosθ) y b (sin θ cosθ) + y a b (sin θ + cos θ) S89. Ans.(d) S90. Ans.(b) Rs New price of Bike 6,500 57, 600 Rs. S9. Ans. (c) 96 Average number of tourists which go by train S9. Ans. (b) Total tourist of Mumbai89 Total tourist of Masuri795 Difference98 S9. Ans. (a) 85 5% 48 Required percentage S94. Ans.(c) Averge of tourists who go by air68.6 Averge of tourists who go by bus 6. Required difference 6.8 S95. Ans. (c) Required ratio 9:8 96:9 S96. Ans. (d); Total No. of crimes in HP 690 S97. Ans. (b); Ratio 0 : 50 : 5 S98. Ans. (d); S99. Ans. (b); Required % S. Ans. (c); Required difference Page 7