Rs.11,550 has to be divided between A, B and C such that A gets 4/5 of what B gets and B gets 2/3 of what C gets. How much more does C get in comparison to A (in Rs.)?
A7,200
B1,800
C1,170
D2,450
Pick an option to attempt
The Setup: We're splitting the bill, but it's nested. We need to standardize their shares into a single continuous ratio A:B:C to figure out who secured what bag.
Step 1: Write out the individual ratios.
A=54B⟹A:B=4:5.
B=32C⟹B:C=2:3.
Step 2: Combine them into one super-ratio. B is the middleman, so we make B's value equal in both ratios by multiplying.
Multiply A:B by 2→8:10.
Multiply B:C by 5→10:15.
Now they link up perfectly: A:B:C=8:10:15.
Step 3: Find the value of one 'part' of the ratio.
Total parts =8+10+15=33 parts.
33 parts=11550.
1 part=3311550=350.
Step 4: Find the difference between C's bag and A's bag.
C's parts =15. A's parts =8.
Difference =15−8=7 parts.
Value of difference =7×350=2450.
Final Answer: 2450
P's income is Rs.140 more than Q's income and R's income is Rs.80 more than S's. If the ratio of P's and R's incomes is 2:3 and the ratio of Q's and S's incomes is 1:2, then the incomes of P, Q, R and S are, respectively:
A₹260, ₹120, ₹320 and ₹240
B₹300, ₹160, ₹600 and ₹520
C₹400, ₹260, ₹600 and ₹520
D₹320, ₹180, ₹480 and ₹360
Pick an option to attempt
The Setup: Setting up a massive system of linear equations here is total NPC behavior. Since they literally give us all four incomes in the options, the smartest strategy is to vibe check the choices against the constraints until only one survives.
Step 1: Check Constraint 1: P−Q=140 and R−S=80.
(A) 260−120=140 (Pass). 320−240=80 (Pass).
(B) 300−160=140 (Pass). 600−520=80 (Pass).
(C) 400−260=140 (Pass). 600−520=80 (Pass).
(D) 320−180=140 (Pass). 480−360=120 (Fail! 120=80). Eliminate D.
Step 2: Check Constraint 2: Ratio of P:R must be 2:3.
(A) P=260,R=320⟹320260=1613 (Fail! Not 2:3). Eliminate A.
(B) P=300,R=600⟹600300=21 (Fail! Not 2:3). Eliminate B.
(C) P=400,R=600⟹600400=64=32 (Pass!).
Step 3: Just to be absolutely sure, check the final constraint for Option C: Ratio of Q:S must be 1:2.
Q=260,S=520⟹520260=21. It's a perfect match. Option C secures the W.
Final Answer: Rs.400, Rs.260, Rs.600 and Rs.520