2 varieties of tea powders worth ₹250/kg and ₹300/kg are mixed with a third variety of tea powder in the ratio 1 : 1 : 2. If the mixture is worth ₹350/kg, find the price of the third variety tea powder.
- (a)₹500/kg
- (b)₹450/kg
- (c)₹400/kg
- (d)₹425/kg
Answer
Why
Correct — D. Read the ratio as actual weights: 1 kg, 1 kg and 2 kg, so 4 kg of mixture in all.
Cost of the two known varieties:
1 × 250 + 1 × 300 = ₹550
Let the third variety cost x per kg. It supplies 2 kg, so it adds 2x.
Total cost = 550 + 2x over a total weight of 4 kg
The mixture is worth ₹350/kg:
(550 + 2x) ⁄ 4 = 350
550 + 2x = 1400
2x = 850 → x = ₹425/kg → option (d)
Why the others are wrong
- (a)₹500/kg — ₹500 is the answer to a 1 : 1 : 1 mix — (250 + 300 + 500) ⁄ 3 = 350. Here the third variety takes 2 parts of 4, so its price is spread over twice the weight.
- (b)₹450/kg — ₹450 overshoots. Test it: 550 + 2(450) = ₹1,450 across 4 kg is ₹362.50/kg, dearer than the ₹350 the mixture is stated to be worth.
- (c)₹400/kg — ₹400 undershoots. 550 + 2(400) = ₹1,350 across 4 kg is ₹337.50/kg, below the stated ₹350 — every ₹25 on the third variety moves the mixture rate by ₹12.50.
Concept
This is a weighted average, not a plain one. The mixture rate is total cost divided by total weight, so a variety carrying 2 parts pulls the rate twice as hard as one carrying 1 part.
Turning the ratio into kilograms — 1, 1 and 2 — makes the algebra write itself. Alligation reaches the same place faster: the first two varieties average ₹275/kg across their 2 kg, and 2 kg at ₹275 balanced against 2 kg at x about a mean of ₹350 needs x − 350 = 350 − 275 = 75.
Either route lands on ₹425/kg.
Note that the mixture is dearer than both named varieties, which is only possible if the unnamed one is dearer still — a useful sanity check that rules out any option below ₹350 immediately.
Key facts
- Mixture rate = total cost ÷ total weight, so the ratio parts act as weights.
- 1 kg at ₹250 with 1 kg at ₹300 costs ₹550 and averages ₹275/kg.
- A 4 kg mixture worth ₹350/kg must cost ₹1,400 in total.
- The third variety therefore supplies ₹850 across 2 kg, which is ₹425/kg.
Study next
Common traps
- Averaging the three prices as though the ratio were 1 : 1 : 1, which returns ₹500.
- Reading 1 : 1 : 2 as three parts in total instead of four.
- Taking ₹350 as the total value of the mixture rather than its rate per kilogram.
The same weighted average is set on two varieties as well as three.
At 12 Sep 2024, 16:00, Quant Q.21 the mix is 5 kg at ₹4 with 3 kg at ₹6. At 19 Sep 2024, 09:00, Quant Q.2 it is 15 kg of ₹10 wheat with 5 kg of a second type to reach ₹30/kg.
A three-variety ratio, as here, is the same weighted average with one extra term.
Related PYQs
No directly related past PYQ was found.