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

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?

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

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?

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?

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.

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?

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.

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.

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 ?

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.