TYPE-6 (LINEAR RACE) 86. In a 1500 m race, Anil beats Bakul by 150 m and in the same race Bakul beats Charles by 75 in. By what distance does Anil beat Charles? a) 217.50 m b) 200.15 m c) 293.50 m d) 313.75 m 87. In a linear race of 500 m, A can beat B by 50 m and in a race of 600 m, B can beat C by 60 m. By how many metres will A beat C in a race of 400 m ? a) 70 b) 68 c) 76 d) 72 88. A can run 250 m in 25 sec and B in 30 sec. How many metres of start can A give to B in a km race so that the race may end in a dead - heat? a) 169.53 m b) 173.82 m c) 166.67 m d) 186.34 m 89. In a 100-m race, A beats B by 20 m and B beats C by 5 m. in the same race, A beats C by: a) 26 m b) 22 m c) 25 m d) 24 m 90. In a race of 100 m, A beats B by 10m. In a race of 100 m, B beats C by 10 m. By what distance will A beat C in a race of 100 m? a) 19 m b) 21 m c) 18 m d) 20 m 91. In a 1500-m race, if A beats B by 100 m and B beats C by 150 m, then by what distance (in m) does A beat C? a) 140 c) 100 b) 150 d) 240 92. In a 5 km race, S gave a 500 m head start to T. If they finished the race at the same time and the speed of T is 13.5 km/h, the speed of S is: a) 15 km/h c) 17.5 km/h b) 20 km/h d) 16.5 km/h 93. In a 140 m race, Pankaj runs at a speed of 2.5 m/s. He gives a start of 20 m to Arun and still defeats him by 4 seconds. The speed of Arun is: a) 1.75 m/s c) 2 m/s b) 1.25 m/s d) 1.5 m/s 94. In a 400 metre race, A runs at a speed of 16 m/sec. If A gives B a start of 15 metres and still beats him by 10 sec, then what is the speed of B? a) 11 m/sec c) 13 m/sec b) 10 m/sec d) 9 m/sec 95. P gives Q a head-start of 2 seconds in a 400 m race, but both finish the race at the same time. Find the time taken by P to finish the race if the speed of Q is 2 m/sec. a) 198 seconds b) 199 seconds c) 200 seconds d) 195 seconds

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Asked on March 22, 2026Mathematics

This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.

Accepted Answer · 2026-03-22T09:32:43.400Z

86. Step 1: When Anil finishes 1500 m, Bakul runs 1500 - 150 = 1350 m. Thus, (v_A)/(v_B) = (1500)/(1350) = (10)/(9). Step 2: When Bakul finishes 1500 m, Charles runs 1500 - 75 = 1425 m. Thus, (v_B)/(v_C) = (1500)/(1425) = (20)/(19). Step 3: (v_A)/(v_C) = (10)/(9) × (20)/(19) = (200)/(171). So, (v_C)/(v_A) = (171)/(200). Step 4: When Anil runs 1500 m, Charles runs 1500 × (171)/(200) = 1282.5 m. Anil beats Charles by 1500 - 1282.5 = 217.5 m. a) 217.50 m 87. Step 1: In 500 m race, A beats B by 50 m, so when A runs 500 m, B runs 450 m. (v_A)/(v_B) = (500)/(450) = (10)/(9). Step 2: In 600 m race, B beats C by 60 m, so when B runs 600 m, C runs 540 m. (v_B)/(v_C) = (600)/(540) = (10)/(9). Step 3: (v_A)/(v_C) = (10)/(9) × (10)/(9) = (100)/(81). (v_C)/(v_A) = (81)/(100). Step 4: In 400 m race, when A runs 400 m, C runs 400 × (81)/(100) = 324 m. A beats C by 400 - 324 = 76 m. c) 76 88. Step 1: Speed of A: v_A = (250)/(25) = 10 m/s. Speed of B: v_B = (250)/(30) ≈ 8.333 m/s. Step 2: In 1000 m race for dead heat, let start given to B be x m. B runs 1000 - x m in time A runs 1000 m. t = (1000)/(10) = 100 s. Step 3: (1000 - x)/(v_B) = 100. 1000 - x = 100 × (250)/(30) = 100 × (25)/(3) ≈ 833.333. x = 1000 - 833.333 = 166.667 m. c) 166.67 m 89. Step 1: A beats B by 20 m in 100 m, so when A runs 100 m, B runs 80 m. (v_A)/(v_B) = (100)/(80) = (5)/(4). Step 2: B beats C by 5 m in 100 m, so when B runs 100 m, C runs 95 m. (v_B)/(v_C) = (100)/(95) = (20)/(19). Step 3: (v_A)/(v_C) = (5)/(4) × (20)/(19) = (25)/(19). (v_C)/(v_A) = (19)/(25). Step 4: When A runs 100 m, C runs 100 × (19)/(25) = 76 m. A beats C by 100 - 76 = 24 m. d) 24 m 90. Step 1: A beats B by 10 m in 100 m, so when A runs 100 m, B runs 90 m. (v_A)/(v_B) = (100)/(90) = (10)/(9). Step 2: B beats C by 10 m in 100 m, so when B runs 100 m, C runs 90 m. (v_B)/(v_C) = (100)/(90) = (10)/(9). Step 3: (v_A)/(v_C) = (10)/(9) × (10)/(9) = (100)/(81). (v_C)/(v_A) = (81)/(100). Step 4: When A runs 100 m, C runs 100 × (81)/(100) = 81 m. A beats C by 100 - 81 = 19 m. a) 19 m 91. Step 1: A beats B by 100 m in 1500 m, so when A runs 1500 m, B runs 1400 m. (v_A)/(v_B) = (1500)/(1400) = (15)/(14). Step 2: B beats C by 150 m in 1500 m, so when B runs 1500 m, C runs 1350 m. (v_B)/(v_C) = (1500)/(1350) = (10)/(9). Step 3: (v_A)/(v_C) = (15)/(14) × (10)/(9) = (25)/(21). (v_C)/(v_A) = (21)/(25). Step 4: When A runs 1500 m, C runs 1500 × (21)/(25) = 1260 m. A beats C by 1500 - 1260 = 240 m. d) 240 92. Step 1: Race is 5 km, T gets 500 m = 0.5 km head start. T runs 4.5 km at 13.5 km/h. Time t = (4.5)/(13.5) = (1)/(3) h. Step 2: S runs 5 km in t. v_S = (5)/(1/3) = 15 km/h. a) 15 km/h 93. Step 1: Pankaj's time for 140 m: t_P = (140)/(2.5) = 56 s. Step 2: Arun gets 20 m start, runs 120 m. Pankaj beats by 4 s, so Arun's time for 120 m is 56 + 4 = 60 s. Step 3: Arun's speed v_A = (120)/(60) = 2 m/s. c) 2 m/s 94. Step 1: A's time for 400 m: t_A = (400)/(16) = 25 s. Step 2: B gets 15 m start, runs 385 m. A beats by 10 s, so B's time for 385 m is 25 + 10 = 35 s. Step 3: B's speed v_B = (385)/(35) = 11 m/s. a) 11 m/sec 95. Step 1: Q's head start in 2 s at 2 m/s: 2 × 2 = 4 m. Step 2: Q runs remaining 400 - 4 = 396 m at 2 m/s. Time t = (396)/(2) = 198 s. Step 3: P runs 400 m in 198 s. a) 198 seconds

Accepted Answer · 2026-03-22T09:32:43.400Z

86. Step 1: When Anil finishes 1500 m, Bakul runs 1500 - 150 = 1350 m. Thus, (v_A)/(v_B) = (1500)/(1350) = (10)/(9). Step 2: When Bakul finishes 1500 m, Charles runs 1500 - 75 = 1425 m. Thus, (v_B)/(v_C) = (1500)/(1425) = (20)/(19). Step 3: (v_A)/(v_C) = (10)/(9) × (20)/(19) = (200)/(171). So, (v_C)/(v_A) = (171)/(200). Step 4: When Anil runs 1500 m, Charles runs 1500 × (171)/(200) = 1282.5 m. Anil beats Charles by 1500 - 1282.5 = 217.5 m. a) 217.50 m 87. Step 1: In 500 m race, A beats B by 50 m, so when A runs 500 m, B runs 450 m. (v_A)/(v_B) = (500)/(450) = (10)/(9). Step 2: In 600 m race, B beats C by 60 m, so when B runs 600 m, C runs 540 m. (v_B)/(v_C) = (600)/(540) = (10)/(9). Step 3: (v_A)/(v_C) = (10)/(9) × (10)/(9) = (100)/(81). (v_C)/(v_A) = (81)/(100). Step 4: In 400 m race, when A runs 400 m, C runs 400 × (81)/(100) = 324 m. A beats C by 400 - 324 = 76 m. c) 76 88. Step 1: Speed of A: v_A = (250)/(25) = 10 m/s. Speed of B: v_B = (250)/(30) ≈ 8.333 m/s. Step 2: In 1000 m race for dead heat, let start given to B be x m. B runs 1000 - x m in time A runs 1000 m. t = (1000)/(10) = 100 s. Step 3: (1000 - x)/(v_B) = 100. 1000 - x = 100 × (250)/(30) = 100 × (25)/(3) ≈ 833.333. x = 1000 - 833.333 = 166.667 m. c) 166.67 m 89. Step 1: A beats B by 20 m in 100 m, so when A runs 100 m, B runs 80 m. (v_A)/(v_B) = (100)/(80) = (5)/(4). Step 2: B beats C by 5 m in 100 m, so when B runs 100 m, C runs 95 m. (v_B)/(v_C) = (100)/(95) = (20)/(19). Step 3: (v_A)/(v_C) = (5)/(4) × (20)/(19) = (25)/(19). (v_C)/(v_A) = (19)/(25). Step 4: When A runs 100 m, C runs 100 × (19)/(25) = 76 m. A beats C by 100 - 76 = 24 m. d) 24 m 90. Step 1: A beats B by 10 m in 100 m, so when A runs 100 m, B runs 90 m. (v_A)/(v_B) = (100)/(90) = (10)/(9). Step 2: B beats C by 10 m in 100 m, so when B runs 100 m, C runs 90 m. (v_B)/(v_C) = (100)/(90) = (10)/(9). Step 3: (v_A)/(v_C) = (10)/(9) × (10)/(9) = (100)/(81). (v_C)/(v_A) = (81)/(100). Step 4: When A runs 100 m, C runs 100 × (81)/(100) = 81 m. A beats C by 100 - 81 = 19 m. a) 19 m 91. Step 1: A beats B by 100 m in 1500 m, so when A runs 1500 m, B runs 1400 m. (v_A)/(v_B) = (1500)/(1400) = (15)/(14). Step 2: B beats C by 150 m in 1500 m, so when B runs 1500 m, C runs 1350 m. (v_B)/(v_C) = (1500)/(1350) = (10)/(9). Step 3: (v_A)/(v_C) = (15)/(14) × (10)/(9) = (25)/(21). (v_C)/(v_A) = (21)/(25). Step 4: When A runs 1500 m, C runs 1500 × (21)/(25) = 1260 m. A beats C by 1500 - 1260 = 240 m. d) 240 92. Step 1: Race is 5 km, T gets 500 m = 0.5 km head start. T runs 4.5 km at 13.5 km/h. Time t = (4.5)/(13.5) = (1)/(3) h. Step 2: S runs 5 km in t. v_S = (5)/(1/3) = 15 km/h. a) 15 km/h 93. Step 1: Pankaj's time for 140 m: t_P = (140)/(2.5) = 56 s. Step 2: Arun gets 20 m start, runs 120 m. Pankaj beats by 4 s, so Arun's time for 120 m is 56 + 4 = 60 s. Step 3: Arun's speed v_A = (120)/(60) = 2 m/s. c) 2 m/s 94. Step 1: A's time for 400 m: t_A = (400)/(16) = 25 s. Step 2: B gets 15 m start, runs 385 m. A beats by 10 s, so B's time for 385 m is 25 + 10 = 35 s. Step 3: B's speed v_B = (385)/(35) = 11 m/s. a) 11 m/sec 95. Step 1: Q's head start in 2 s at 2 m/s: 2 × 2 = 4 m. Step 2: Q runs remaining 400 - 4 = 396 m at 2 m/s. Time t = (396)/(2) = 198 s. Step 3: P runs 400 m in 198 s. a) 198 seconds

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