Olympiad Test : Simplification - Class 6 MCQ

Suppose their paths cross after x minutes.
Then, 11 + 57x = 51 – 63x
⇒ 120x = 40
⇒ x =1/3
Number of floors covered by David in (1/3) min. =1/3 × 57= 19.
So, their paths cross at (11 +19) i.e., 30^th floor.

Let a = 469
b = 469 there
given expression 
=  4ab/ab
=  4

Let the number of hens be x and the number of cows be y.
Then, x + y = 48.... (i) and 2x + 4y = 140
⇒ x + 2y = 70 .... (ii)
Solving (i) and (ii) we get: x = 26, y = 22.
∴ The required answer = 26.

Let total number of children be x.
Then, x × (1/8) x = x/2 × 16  ⇔ x = 64
∴ Number of notebooks = x²/8
=1/8 × 64 × 64 = 512

Suppose the man works overtime for x hours.
Now, working hours in 4 weeks = (5 × 8 × 4) = 160
∴ 160 × 2.40 + x × 3.20 = 432
⇒ 3.20x = 432 – 384 = 48
⇒ x = 15
Hence, total hours of work = (160 + 15) = 175

Let the capacity of 1 bucket = x
Then, the capacity of tank = 25x
New capacity of bucket = 2x/5
∴ Required number of buckets
= 25x/ (2x/5) =125/2 = 62.5

Original share of 1 person =1/8
New share of 1 person =1/7
Increase = 1/7 – 1/8 = 1/56
∴ Required fraction = (1/56) / (1/8) = 1/7

Let the total number of shots be x. Then,
Shots fired by A    = 5x/8
Shots fired by B    = 3x/8
Killing shots by A = 1/3 of 5x/8 = 5x/24
Shots missed by B = 1/2 of 3x/8 = 3x/16
∴ 3x/16= 27 or x = 144
Birds killed by A = 5x/24 = (5x 144)/24 = 30

Let savings in N.S.C and P.P.F. be Rs x and Rs.
(150000 – x) respectively. Then,
1/3x =1/2(150000 – x)
⇒ x/3 + x/2 = 75000
⇒ 5x/6 = 75000
⇒ x = (75000 × 6)/5 = Rs = 90000
∴ Savings in Public Provident Fund
= Rs (1 50000 – 90000) = Rs 60000

Let C’s share = Rs x
Then, B’s share = Rs x/4,
A’s share = Rs 2/3 × x/4    = Rs x/6
⇒ 17x/12 = 1360
⇒ x = (1360 × 12)/17= Rs 960
Hence, B’s share = Rs 960/4 = Rs 240