IPMAT Indore 2026 · Quantitative Ability · Set 2: Nutritionist’s diet plan – Calcium, Iron and Protein

Step 1 — total each nutrient across one serving of all five items.

\text{Calcium}=300+90+210+120+50=770\text{mg}

\text{Iron}=0+6+4+3+1=14\text{mg}

\text{Protein}=8+3+6+5+4=26 g

Step 2 — convert each to a percentage of its MDR.

Step 3 — pick the smallest. Protein, at 65\%.

Answer: Option 1 — Protein with 65% MDR

Shortcut. Only two options are even internally consistent — Calcium is 770/1100=70\% and Protein is 26/40=65\%, so options (b) and (d) are wrong on their own numbers. That leaves comparing 65\% against 70\%.

Step 1 — write the three requirements. Milk gives \left( 300,\,0,\,8 \right) and Rice gives \left( 50,\,1,\,4 \right) per serving:

\text{Calcium:}300x+50y\ge 1100

\text{Iron:}0x+1y\ge 15

\text{Protein:}8x+4y\ge 40

Step 2 — the iron row decides y immediately. Milk contains no iron, so all 15 mg must come from rice:

y\ge 15

Step 3 — now use calcium. With y=15:

300x+750\ge 1100 \Rightarrow 300x\ge 350 \Rightarrow x\ge 1.17 \Rightarrow x=2

(servings must be whole numbers)

Step 4 — check protein.

8\left( 2 \right)+4\left( 15 \right)=16+60=76 \ge 40 ✓

Step 5 — total.

x+y=2+15=17

Worth noting: \left( x,y \right)=\left( 1,16 \right) also works and also totals 17 — calcium comes to exactly 300+800=1100. Either way the minimum is 17.

Answer: Option 2 — 17

Shortcut. Milk’s zero in the iron column is the whole question: it forces y\ge 15 before you look at anything else. Then calcium needs only one or two servings of milk, and protein is never binding.

Step 1 — work out the 15% thresholds.

\text{Calcium:}0.15\times 1100=165\text{mg}

\text{Iron:}0.15\times 15=2.25\text{mg}

\text{Protein:}0.15\times 40=6 g

Step 2 — test each food item against all three.

Step 3 — count those reaching at least two. Milk and Almonds.

2

Answer: Option 1 — 2

Shortcut. Compute the three thresholds once (165, 2.25, 6) and then it is pure table-scanning. Almonds clears all three; Milk clears two; nothing else manages more than one. Note protein for Almonds is exactly 6 — “at least” means it counts.

Step 1 — half the MDR.

\text{Calcium}550, \text{Iron}7.5, \text{Protein}20

Step 2 — multiply each item by the maximum 7 servings and test all three.

Step 3 — read off. Spinach, Almonds and Oats all manage it.

Milk fails only on iron (it has none), and Rice fails on calcium and iron.

Answer: Option 2 — Only Almonds, Spinach, and Oats

Shortcut. Test the weakest nutrient of each item first and you can reject fast: milk dies on iron (zero), rice on calcium (7\times 50=350<550). Spinach looks weak on protein but 7\times 3=21 just clears 20 — that near-miss is the question’s trap.

Step 1 — what the two milk servings provide.

2\times \left( 300, 0, 8 \right)=\left( 600\text{mg Ca}, 0\text{mg Fe}, 16\text{g protein}\right)

Step 2 — the shortfall against the MDR.

\text{Calcium:}1100-600=500 \text{Iron:}15-0=15 \text{Protein:}40-16=24

Step 3 — for each remaining item, find how many servings k clear all three.

Each item needs the largest of its three requirements, rounded up.

Step 4 — take the smallest across items. Almonds, with 4 servings.

Answer: Option 3 — 4

Shortcut. Milk contributes no iron, so whichever item you choose must supply all 15 mg — that alone rules Rice out. Almonds is the obvious candidate (best iron-per-serving among the calcium-rich items), and checking it first gives 4 immediately.