# Online Aptitude Test 1

#### Q 1. What was the day of the week on 26-January-1950?

Correct! Wrong!

Explanation: Formula:-(Date + Month code + No.of years + No.of leap year + Century code)/7 = (26 + 1 + 50 + 12 + 0)/7 = 84/7 = 5 = Thursday

#### Q 2. A train moves past a telegraph post and a bridge 264 m long in 8 seconds and 20 seconds respectively. What is the speed of the train?

Correct! Wrong!

Explanation: Let the length of the train be x meters and its speed by y m/sec. Then, x/y = 8 => x = 8y Now, [(x + 264)/20] = y => 8y + 264 = 20y => y = 22 ∴ Speed = 22 m/sec = [22 × (18/5)] km/hr = 79.2 km/hr.

#### Q 3. The perimeters of two squares are 40 cm and 32 cm. Find the perimeter of a third square whose area is equal to the difference of the areas of the two squares

Correct! Wrong!

Explanation: We know perimeter of square = 4(side) So Side of first square = 40/4 = 10 cm Side of second square = 32/4 = 8 cm Area of third Square = 10*10 – 8*8 = 36 cm So side of third square = 6 [because area of square = side*side] Perimeter = 4*Side = 4*6 = 24 cm

#### Q 4. What percentage of numbers from 1 to 70 have 1 or 9 in the unit’s digit?

Correct! Wrong!

Explanation: Clearly, the numbers which have 1 or 9 in the unit’s digit, have squares that end in the digit 1. Such numbers from 1 to 70 are 1, 9, 11, 19, 21, 29, 31, 39, 41, 49, 51, 59, 61, 69. Number of such number =14 Required percentage = (14/70 x 100)% = 20%.

#### Q 5. The average weight of 25 boys in a class is 48 kgs. The average weight of the class of 40 students is 45 kgs. What is the average weight of the 15 girls in the class?

Correct! Wrong!

Explanation: otal weight of boys in the class = 25 *48 = 1200 kgs Total weight of all students in the class = 45 * 40 = 1800 kgs Total weight of the girls in the class = 1800 – 1200 = 600 kgs Average weight of girls = 600/15 = 40 kgs

#### Q 6. A rectangular block 6 cm by 12 cm by 15 cm is cut up into an exact number of equal cubes. Find the least possible number of cubes.

Correct! Wrong!

Explanation: Volume of the block = (6 x 12 x 15) cu.cm = 1080 cu.cm Side of the largest cube = H.C.F. of 6 cm, 12 cm, 15 cm = 3 cm. Volume of this cube = (3 x 3 x 3) cu.cm = 27 cu.cm Number of cubes = 1080/27 = 40.

#### Q 7. A and B can do a piece of work in 40 days, B and C can do it in 120 days. If B alone can do it in 180 days, in how many days will A and C do it together?

Correct! Wrong!

Explanation: A + B take 40 days. B alone takes 180 days. ∴ A will take 1/40 – 1/180 = 7/360 ⇒ 360/7 days. B + C take 120 days. ∴ C alone will take 1/120 – 1/180 = 1/360 i.e. 360 days. ∴ A & C together will take 7/360 + 1/360 = 8/360 ⇒ 360/8 = 45 days to complete the work.

#### Q 8. The present ratio of ages of A and B is 4:5. 18 years ago, this ratio was 11:16. Find the sum total of their present ages.

Correct! Wrong!

Explanation: Let present age of A and B be 4x and 5x. 18 years ago their ages; (4x-18)/(5x-18) = 11/16; Or, 64x-288 = 55x-198; Or, 64x-55x = -198+288; Or, 9x = 90; Or, x = 90/9 = 10; Sum of the present ages = 40+50 = 90 years.

#### Q 9. Find the rate of the stream, if a boat covers 120 km downstream and 40 km upstream in 4 hours.

Correct! Wrong!

Explanation: Distance covered in downstream = 120 km Time taken in downstream = 4 hours. Rate of downstream = distance / time = a = 120km / 4 hours = 30 km/hr. Distance covered in upstream = 40 km Since it takes same time to cover this 40km, Time taken in upstream = 4 hours. Rate of upstream = distance / time = b = 40km / 4 hours = 10 km/hr. Speed of stream = (a – b)/2 = (1/2)(30 – 10) km/hr = 10 km/hr.

#### Q 10. A vertical toy 18 cm long casts a shadow 8 cm long on the ground. At the same time a pole casts a shadow 48 m. long on the ground. Then find the height of the pole ?

Correct! Wrong!

Explanation: We know the rule that, At the particular time for all object, the ratio of height and shadow are same. Let the height of the pole be ‘H’ Then, 18/8 = H/48 => H = 108 m.