These questions wrap a profit margin around a normal mixing problem. The trick is to peel off the profit first: alligation works on cost price, never on selling price.
Selling price back to cost price, then alligate
If a mixture sells at SP for a profit of p%, its true cost price is:
CP=100+pSP×100
That CP is the mean of the mixture. Now run the ordinary cross between the two ingredient prices and this CP to get the ratio. The whole question is a plain alligation with one extra SP→CP step.
• Gain/loss on a sold mix: find the mean CP by weighted average, then %=CPSP−CP×100.
• Splitting a stock or loan: the overall rate is the weighted average of the two rates — alligate the two rates around the overall rate to get the split.
⚖️Alligation LabCross rule & replacement
Cheaper (c)
Dearer (d)
Mean (m)
Try a classic
cheaper : dearer=6 : 4=3 : 2
Mix 3 parts cheaper with 2 parts dearer
Distance intuition
m sits CLOSER to the cheaper (gap 4 vs 6) → the mix is mostly CHEAPER. Each ingredient's share is the distance to the OTHER value — the inverse-distance rule.
Sell a mix at ₹66 for a 10% profit ⇒ CP =11066×100= ₹, and that ₹60 is what you alligate.
📝Practice Questions
Q1Tea at ₹50 and ₹70 per kg is mixed and sold at ₹66/kg at 10% profit. The mixing ratio is:
Q2Pulses at ₹70 and ₹90 per kg are mixed 1:1 and sold at ₹88/kg. The profit percent is:
Q3₹12,000 is lent at 5% and 8% simple interest; total interest is ₹810 a year. The sum lent at 8% is:
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Real exam questions — Pricing, Profit & Loss
3 question types · 9 solved examples from real SSC papers
Profit is a smokescreen: convert the selling price back to cost price first, then alligate exactly as usual. Splitting a stock or a loan uses the very same cross.
How to solve this type
The selling price and the profit% are a smokescreen — first convert them into the mixture’s COST price: CP =100+profit%SP×100. That CP is the true mean price of the mixture. Now run the ordinary alligation cross between the two ingredient prices and this CP to get the mixing ratio. The only extra step over a plain ratio question is that first SP→CP conversion.
In what ratio should a grocer mix tea at ₹26 and ₹32 per kg so that by selling the mixture at ₹30 per kg he gains 10%?
A7 : 26B16 : 7C26 : 7D7 : 16
In what ratio should wheat at ₹23 per kg be mixed with wheat at ₹14 per kg so that selling the mixture at ₹20 per kg gives a 25% profit?
A5 : 7B3 : 5C2 : 3D2 : 7
In what ratio should tea at ₹60 per kg be mixed with tea at ₹70 per kg so that selling the mixture at ₹80 per kg gives a 25% profit?
