Mathematics Archives

371. A rectangular field 30 m long and 20 m broad. How much deep it should be dug so that from the earth taken out, a platform can be formed which is 8 m long, 5.5 m broad and 1.5 m high where as the earth taken out is increase by 10/5?

A. 12 cm

B. 10 cm

C. 18 cm

D. 24 cm

✅ The correct answer is option B. 10 cm.
30 * 20 * x = (8 * 5.5 * 1.5)/2

372. A batsman in his 17th innings makes a score of 85 and their by increasing his average by 3. What is his average after the 17th innings?

A. 34

B. 35

C. 36

D. 37

✅ The correct answer is option D. 37.
16x + 85 = 17(x + 3)

373. At 10 a.m. two trains started traveling toward each other from stations 287 miles apart. They passed each other at 1:30 p.m. the same day. If the average speed of the faster train exceeded the average speed of the slower train by 6 miles per hour, which of the following represents the speed of the faster train, in miles per hour?

A. 38

B. 40

C. 44

D. 48

✅ The correct answer is option C. 44.
Let the speed of the faster train be x miles per hour and

the distance travelled by it when it meets the slower train be y miles. Time taken by the faster train to cover y miles

= Time taken by the slower train to cover (287-y) miles

= 3.5 hours (y/x) = (287-y)/(x-6) = 3.5 Solving, x = 44 miles/hr

374. Rs.8000 become Rs.9261 in a certain interval of time at the rate of 5% per annum of C.I. Find the time?

A. 4 years

B. 6 years

C. 2 years

D. 3 years

✅ The correct answer is option D. 3 years.

375. When 2 is added to half of one-third of one-fifth of a number, the result is one-fifteenth of the number. Find the number?

A. 40

B. 50

C. 60

D. 70

✅ The correct answer is option C. 60.

376. The true discount on a bill due 9 months hence at 16% per annum is Rs. 189. The amount of the bill is:

A. Rs. 1386

B. Rs. 1764

C. Rs. 1575

D. Rs. 2268

✅ The correct answer is option B. Rs. 1764.

377. The diameter of a circle is 105 cm less than the circumference what is the diameter of the circle?

A. 44 cm

B. 46 cm

C. 48 cm

D. 49 cm

✅ The correct answer is option D. 49 cm.

378. 8 litres are drawn from a cask full of wine and is then filled with water. This operation is performed three more times. The ratio of the quantity of wine now left in cask to that of water is 16 : 65. How much wine did the cask hold originally?

A. 18 litres

B. 24 litres

C. 32 litres

D. 42 litres

✅ The correct answer is option B. 24 litres.

379. If a and b are the roots of the equation x2 – 9x + 20 = 0, find the value of a2 + b2 + ab?

A. -21

B. 1

C. 61

D. 21

✅ The correct answer is option C. 61.